Probability practice · Easy

A man and his wife appear for an interview for two posts. The probability of the man’s selection is 1/5 and that of his wife’s selection is 1/7. The probability that at least one of them is selected, is

A die is tossed twice. The probability of having a number greater than 4 on each toss is

A bag A contains 2 white and 3 red balls, and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and it is found to be red. Let $p$ be the probability that it was drawn from the bag B then find the value of $\left[\frac{1}{p}\right]$ where [.] denotes G.I.F.

Three persons, A, B and $\mathrm{C}$, fire at a target in turn, starting with $\mathrm{A}$. Their probability of hitting the target are $0.4,0.3$ and 0.2 respectively. The probability of two hits is

If $n$ integers taken at random are multiplied together, then the probability that the last digit of the product is 1, 3, 7 or 9, is

The probability of getting the sum more than 7 when a pair of dice is tossed is

$'X'$ speaks truth in 60% and $'Y'$ in 50% of the cases. The probability that they contradict each other narrating the same incident is

Two coins and a die are tossed. The probability that both coins fall heads and the die shows a 3 or 6, is

The probability that in a family of 5 members, exactly 2 members have birthday on sunday, is

Let a die is loaded in such a way that prime number faces are twice as likely to occur as a non-prime number faces. Then, the probability that an odd number will be show up when the die is tossed, is

Two non-negative integers $x$ and $y$ are chosen at random with replacement. The probability that $x^2+y^2$ is divisible by 10, is

A dice is rolled three times. The probability of getting a larger number than the previous number each time is

Four persons are selected from a group of 4 men, 2 women and 3 children. The probability that exactly two of them are men is

Girl students constitute $10 \%$ of I year and $5 \%$ of II year at Roorkee University. During summer holidays $70 \%$ of the I year and $30 \%$ of II year students are given a project. The girls take turns on duty in canteen. The chance that I year girl student is on duty in a randomly selected day is

If $P\left( A \right) = P\left( B \right) = x$ and $P\left( {A \cap B} \right) = P\left( {A' \cap B'} \right) = \frac{1}{3}$, then $x$ is equal to

A five digit number is formed by writing the digits 1, 2, 3, 4, 5, in a random order without repetitions. Then the probability that the number is divisible by 4, is

Let $A$ and $B$ be independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{6}$. Then,

An integer is chosen at random from first two hundred digits. Then, the probability that the integer chosen is divisible by 6 or 8, is

Consider 5 independent Bernulli's trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then $p$ lies in the interval:

If $(1+3 p) / 3,(1-p) / 4$ and $(1-2 p) / 2$ are the probabilities of three mutually exclusive events, then the set of all values of $p$ is

If $P\left( {A \cap B} \right) = \frac{1}{2},P\left( {\bar A \cap \bar B} \right) = \frac{1}{3},P\left( A \right) = p,P\left( B \right) = 2\;p,$ then the value of $p$ is given by

In a bag there are 20 cards 10 names $A$ and another 10 names B. Cards are drawn randomly one by one with replacement, the probability that second $A$ comes before third $B$ is

A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then probability that both are dead is

Twenty five coins are tossed simultaneously. The probability that the fifth coin will fall with head upward, is

If $P\left( {A \cap B} \right) = \frac{1}{3},\;P\left( {A \cup B} \right) = \frac{5}{6},\;$ and $P\left( A \right) = \frac{1}{2}$ then which one of the following is correct?

Ram and Shyam throw with one dice for a prize of Rs. 88 which is to be won by the player who throws 1 first. If Ram starts, then mathematical expectation for Shyam is

The probability that Krishna will be alive 10 year hence is $\frac{7}{15}$ and Hari will be alive is $\frac{7}{10}$. The probability that both Krishna and Hari will be dead 10 years hence is

Suppose $A$ is a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are chosen at random. If the probability that $P$ is a subset of $Q$ is $243 / 1024$, then $n$ is equal to

If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is

A and B are two independent events. The probability that both $\mathrm{A}$ and $\mathrm{B}$ occur is $1 / 6$ and the probability that at least one of them occurs is $2 / 3$. Find $8 \mathrm{P}(\mathrm{A})+9 \mathrm{P}(\mathrm{B})$ if $\mathrm{P}(\mathrm{A})>$ $\mathrm{P}(\mathrm{B})$.