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Probability

141 Questions
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET
1992 JEE Advanced MCQ
IIT-JEE 1992
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting, points $0,$ $1$ and $2$ are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are independent, the probability of India getting at least $7$ points is
A.
$0.8750$
B.
$0.0875$
C.
$0.0625$
D.
$0.0250$
1992 JEE Advanced Numerical
IIT-JEE 1992
A lot contains $50$ defective and $50$ non defective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events $A, B, C$ are defined as
$A=$ (the first bulbs is defective)
$B=$ (the second bulbs is non-defective)
$C=$ (the two bulbs are both defective or both non defective)
Determine whether
(i) $\,\,\,\,\,$ $A, B, C$ are pairwise independent
(ii)$\,\,\,\,\,$ $A, B, C$ are independent
1992 JEE Advanced Numerical
IIT-JEE 1992
Three faces of a fair die are yellow, two faces red and one blue. The die is tossed three times. The probability that the colours, yellow, red and blue, appear in the first, second and the third tosses respectively is ...............
1991 JEE Advanced MSQ
IIT-JEE 1991
For any two events $A$ and $B$ in a simple space
A.
$P\left( {A/B} \right) \ge {{P\left( A \right) + P\left( B \right) - 1} \over {P\left( B \right)}},P\left( B \right) \ne 0$ is always true
B.
$P\left( {A \cap \overline B } \right) = P\left( A \right) - P\left( {A \cap B} \right)\,\,$ does not hold
C.
$P\left( {A \cup B} \right) = 1 - P\left( {\overline A } \right)P\left( {\overline B } \right),$ if $A$ and $B$ are independent
D.
$P\left( {A \cup B} \right) = 1 - P\left( {\overline A } \right)P\left( {\overline B } \right),$ if $A$ and $B$ are disjoint.
1991 JEE Advanced Numerical
IIT-JEE 1991
In a test an examine either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he make a guess is $1/3$ and the probability that he copies the answer is $1/6$. The probability that his answer is correct given that he copied it, is $1/8$. Find the probability that he knew the answer to the questions given that he correctly answered it.
1991 JEE Advanced Numerical
IIT-JEE 1991
If the mean and the variance of binomial variate $X$ are $2$ and $1$ respectively, then the probability that $X$ takes a value greater than one is equal to ...............
1990 JEE Advanced Numerical
IIT-JEE 1990
A is a set containing $n$ elements. $A$ subset $P$ of $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P.$ $A$ subset $Q$ of $A$ is again chosen at random. Find the probability that $P$ and $Q$ have no common elements.
1990 JEE Advanced Numerical
IIT-JEE 1990
Let $A$ and $B$ be two events such that $P\,\,\left( A \right)\,\, = \,\,0.3$ and $P\left( {A \cup B} \right) = 0.8.$ If $A$ and $B$ are independent events then $P(B)=$ ................
1989 JEE Advanced MSQ
IIT-JEE 1989
If $E$ and $F$ are independent events such that $0 < P\left( E \right) < 1$ and $0 < P\left( F \right) < 1,$ then
A.
$E$ and $F$ are mutually exclusive
B.
$E$ and ${F^c}$ (the complement of the event $F$) are independent
C.
${E^c}$ and ${F^c}$ are independent
D.
$P\left( {E|F} \right) + P\left( {{E^c}|F} \right) = 1.$
1989 JEE Advanced Numerical
IIT-JEE 1989
Suppose the probability for A to win a game against B is $0.4.$ If $A$ has an option of playing either a "best of $3$ games" or a "best of $5$ games" match against $B$, which option should be choose so that the probability of his winning the match is higher ? (No game ends in a draw).
1989 JEE Advanced Numerical
IIT-JEE 1989
A pair of fair dice is rolled together till a sum of either $5$ or $7$ is obtained. Then the probability that $5$ comes before $7$ is ...............
1989 JEE Advanced MCQ
IIT-JEE 1989
If the probability for $A$ to fail in an examination is $0.2$ and that for $B$ is $0.3$, then the probability that either $A$ or $B$ fails is $0.5$
A.
TRUE
B.
FALSE
1988 JEE Advanced MCQ
IIT-JEE 1988
One hundred identical coins, each with probability, $p,$ of showing up heads are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins, then the value of $p$ is
A.
$1/2$
B.
$49/101$
C.
$50/101$
D.
$51/101.$
1988 JEE Advanced MSQ
IIT-JEE 1988
For two given events $A$ and $B,$ $P\left( {A \cap B} \right)$
A.
not less than $P\left( A \right) + P\left( B \right) - 1$
B.
not greater than $P\left( A \right) + P\left( B \right)$
C.
equal to $P\left( A \right) + P\left( B \right) - P\left( {A \cup B} \right)\,\,$
D.
$P\left( A \right) + P\left( B \right) + P\left( {A \cup B} \right)\,\,$
1988 JEE Advanced Numerical
IIT-JEE 1988
A box contains $2$ fifty paise coins, $5$ twenty five paise coins and a certain fixed number $N\,\,\left( { \ge 2} \right)$ of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these $5$ coins is less than one rupee and fifty paise.
1988 JEE Advanced Numerical
IIT-JEE 1988
Urn $A$ contains $6$ red and $4$ black balls and urn $B$ contains $4$ red and $6$ black balls. One ball is drawn at random from urn $A$ and placed in urn $B$. The one ball is drawn at random from urn $B$ and placed in urn $A$. If one ball is now drawn at random from urn $A$, the probability that it is found to be red is ................
1987 JEE Advanced Numerical
IIT-JEE 1987
A man takes a step forward with probability $0.4$ and backwards with probability $0.6$ Find the probability that at the end of eleven steps he is one step away from the starting point.
1986 JEE Advanced MCQ
IIT-JEE 1986
A student appears for tests, $I$, $II$ and $III$. The student is successful if he passes either in tests $I$ and $II$ or tests $I$ and $III$. The probabilities of student passing in tests $I$, $II$ and $III$ are $p, q$ and ${1 \over 2}$ respectively. If the probability that the student is successful is ${1 \over 2}$, then
A.
$p=q=1$
B.
$p = q = {1 \over 2}$
C.
$p=1,$ $q=0$
D.
$p = 1,q = {1 \over 2}$
1986 JEE Advanced MCQ
IIT-JEE 1986
The probability that at least one of the events $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.2,$ then $P\left( {\overline A } \right) + P\left( {\overline B } \right)$ is
A.
$0.4$
B.
$0.8$
C.
$1.2$
D.
$1.4$
1986 JEE Advanced Numerical
IIT-JEE 1986
A lot contains $20$ articles. The probability that the lot contains exactly $2$ defective articles is $0.4$ and the probability that the lot contains exactly $3$ defective articles is $0.6$. Articles are drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is the probability that the testing procedure ends at the twelth testing.
1986 JEE Advanced Numerical
IIT-JEE 1986
If ${{1 + 3p} \over 3},\,\,\,{{1 - p} \over 4}$ and $\,{{1 - 2p} \over 2}$ are the probabilities of three mutually exclusive events, then the set of all values of $p$ is ..............
1985 JEE Advanced Numerical
IIT-JEE 1985
In a multiple-choice question there are four alternative answers, of which one or more are correct. A candidate will get marks in the question only if he ticks the correct answers. The candidate decides to tick the answers at random, If he is allowed upto three chances to answer the questions, find the probability that he will get marks in the questions.
1985 JEE Advanced Numerical
IIT-JEE 1985
A box contains $100$ tickets numbered $1, 2, ....., 100.$ Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than $10.$ The minimum number on them is $5$ with probability ........
1985 JEE Advanced Numerical
IIT-JEE 1985
$P\left( {A \cup B} \right) = P\left( {A \cap B} \right)$ if and only if the relation between $P(A)$ and $P(B)$ is .............
1984 JEE Advanced MCQ
IIT-JEE 1984
A box contains $24$ identical balls of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4$th time on the $7$th draw is
A.
$5/64$
B.
$27/32$
C.
$5/32$
D.
$1/2$
1984 JEE Advanced MCQ
IIT-JEE 1984
Three identical dice are rolled. The probability that the same number will appear on each of them is
A.
$1/6$
B.
$1/36$
C.
$1/18$
D.
$3/28$
1984 JEE Advanced MSQ
IIT-JEE 1984
If $M$ and $N$ are any two events, the probability that exactly one of them occurs is
A.
$P\left( M \right) + P\left( N \right) - 2P\left( {M \cap N} \right)$
B.
$P\left( M \right) + P\left( N \right) - P\left( {M \cap N} \right)$
C.
$P\left( {{M^c}} \right) + P\left( {{N^c}} \right) - 2P\left( {{M^c} \cap {N^c}} \right)$
D.
$P\left( {M \cap {N^c}} \right) + P\left( {{M^c} \cap N} \right)$
1984 JEE Advanced Numerical
IIT-JEE 1984
In a certain city only two newspapers $A$ and $B$ are published, it is known that $25$% of the city population reads $A$ and $20$% reads $B$ while $8$% reads both $A$ and $B$. It is also known that $30$% of those who read $A$ but not $B$ look into advertisements and $40$% of those who read $B$ but not $A$ look into advertisements while $50$% of those who read both $A$ and $B$ look into advertisements. What is the percentage of the population that reads an advertisement?
1983 JEE Advanced MCQ
IIT-JEE 1983
Fifteen coupons are numbered $1, 2 ........15,$ respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is $9,$ is
A.
${\left( {{9 \over {16}}} \right)^6}$
B.
${\left( {{18 \over {15}}} \right)^7}$
C.
${\left( {{3 \over {5}}} \right)^7}$
D.
none of these
1983 JEE Advanced Numerical
IIT-JEE 1983
$A, B, C$ are events such that
$P\left( A \right) = 0.3,P\left( B \right) = 0.4,P\left( C \right) = 0.8$
$P\left( {AB} \right) = 0.08,P\left( {AC} \right) = 0.28;\,\,P\left( {ABC} \right) = 0.09$

If $P\left( {A \cup B \cup C} \right) \ge 0.75,$ then show that $P$ $(BC)$ lies in the interval $0.23 \le x \le 0.48$

1983 JEE Advanced Numerical
IIT-JEE 1983
Cards are drawn one by one at random from a well - shuffled full pack of $52$ playing cards until $2$ aces are obtained for the first time. If $N$ is the number of cards required to be drawn, then show that ${P_r}\left\{ {N = n} \right\} = {{\left( {n - 1} \right)\left( {52 - n} \right)\left( {51 - n} \right)} \over {50 \times 49 \times 17 \times 13}}$ where $2 \le n \le 50$
1983 JEE Advanced MCQ
IIT-JEE 1983
If the letters of the word "Assassin" are written down at random in a row, the probability that no two S's occur together is $1/35$
A.
TRUE
B.
FALSE
1982 JEE Advanced MCQ
IIT-JEE 1982
If $A$ and $B$ are two events such that $P\left( A \right) > 0,$ and $P\left( B \right) \ne 1,$ then $P\left( {{{\overline A } \over {\overline B }}} \right)$ is equal to
A.
$1 - P({A \over B})$ (Here $\overline A $ and $\overline B $ are complements of $A$ and $B$ respectively).
B.
$1 - P({{\overline A } \over B})$ (Here $\overline A $ and $\overline B $ are complements of $A$ and $B$ respectively).
C.
${{1 - P\left( {A \cup B} \right)} \over {P\left( {\overline B } \right)}}$ (Here $\overline A $ and $\overline B $ are complements of $A$ and $B$ respectively).
D.
${{P\left( {\overline A } \right)} \over {P\left( {\overline B } \right)}}$ (Here $\overline A $ and $\overline B $ are complements of $A$ and $B$ respectively).
1982 JEE Advanced Numerical
IIT-JEE 1982
$A$ and $B$ are two candidates seeking admission in $IIT.$ The probability that $A$ is selected is $0.5$ and the probability that both $A$ and $B$ are selected is atmost $0.3$. Is it possible that the probability of $B$ getting selected is $0.9$ ?
1981 JEE Advanced Numerical
IIT-JEE 1981
An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are $0.4, 0.3, 0.2$ and $0.1$ respectively. What is the probability that the gun hits the plane?
1981 JEE Advanced Numerical
IIT-JEE 1981
For a biased die the probabilities for the different faces to turn up are given below : IIT-JEE 1981 Mathematics - Probability Question 136 English

This die tossed and you are told that either face $1$ or face $2$ has turned up. Then the probability that it is face $1$ is ...............

1980 JEE Advanced MCQ
IIT-JEE 1980
Two events $A$ and $B$ have probabilities $0.25$ and $0.50$ respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then the probability that neither $A$ nor $B$ occurs is
A.
$0.39$
B.
$0.25$
C.
$0.11$
D.
none of these
1980 JEE Advanced MCQ
IIT-JEE 1980
The probability that an event $A$ happens in one trial of an experiment is $0.4.$ Three independent trials of the experiment are performed. The probability that the event $A$ happens at least once is
A.
$0.936$
B.
$0.784$
C.
$0.904$
D.
none of these
1979 JEE Advanced MCQ
IIT-JEE 1979
Two fair dice are tossed. Let $x$ be the event that the first die shows an even number and $y$ be the event that the second die shows an odd number. The two events $x$ and $y$ are:
A.
Mutually exclusive
B.
Independent and mutually exclusive
C.
Dependent
D.
None of these.
1979 JEE Advanced Numerical
IIT-JEE 1979
Six boys and six girls sit in a row randomly. Find the probability that
(i) the six girls sit together
(ii) the boys and girls sit alternately.
1978 JEE Advanced Numerical
IIT-JEE 1978
Balls are drawn one-by-one without replacement from a box containing $2$ black, $4$ white and $3$ red balls till all the balls are drawn. Find the probability that the balls drawn are in the order $2$ black, $4$ white and $3$ red.