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Probability

365 Questions
All Exams JEE Mains JEE Advanced
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?
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.
1994 JEE Advanced Numerical
IIT-JEE 1994
If two events $A$ and $B$ are such that $P\,\,\left( {{A^c}} \right)\,\, = \,\,0.3,\,\,P\left( B \right) = 0.4$ and $P\left( {A \cap {B^c}} \right) = 0.5,$ then $P\left( {B/\left( {A \cup {B^c}} \right)} \right.$$\left. \, \right] = $ ............
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 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
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 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 ...............
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 ................
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
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 .............
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 134 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 ...............

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
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