Probability practice · Mixed difficulty

If eight coins are tossed together, then the probability of getting exactly 3 heads is

Three squares of a chess board are chosen at random, the probability that two are of one colour and one of another

If the mean and S.D. of a binomial distribution are 20 and 4 respectively, then the number of trials is

If $P(A)=\frac{4}{5}$ and $P(A \cap B)=\frac{7}{10}$, then $P(B / A)$ is equal to

Two numbers are selected at random from set of the first 100 natural numbers. The probability that the product obtained is divisible by 3 is $\mathrm{k}$ then $\frac{150 \mathrm{k}}{83}$ is equal to

A committee of the five is to be chosen from a group of people. The probability that a certain married couple will either serve together or not at all is

If $E$ and $F$ are two events such that $0 < P(F) < 1$, then

In a bolt factory, machines A, B and C manufacture respectively $20 \%, 30 \%$ and $50 \%$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolts is drawn at random from the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine C is

If the mean and variance of a binomial distribution are 4 and 3 respectively, then $P(X=1)$ is

a bag contains three coins one of which has head on both sides, another is a biased coin that shows up heads $90 \%$ of the time and thnbiased coin a coin is taken oute third one is an unbiased from the bag at random and tossed if it shows up a head then the probablilty tht it is the unbiased coin is

A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. If $p$ denotes the probability that 7 comes before 5 , then $5 p$ is equal

A coffee connoisseur claims that he can distinguish between a cup of instant coffee and a cup of percolator coffee $75 \%$ of time. It is agreed that his claim will be accepted if he correctly identifies at least 5 of the 6 cups. His chances of having the claim accepted is

If $A=\{2,3,4,8,10\}, B=\{3,4,5,10,12\}, C=\{4,5, 6,12,14\}$ then find $(A \cap B) \cup(A \cap C)$.

There are $n$ different objects, 1, 2, 3, $\cdots, n$, distributed at random in $n$ places marked $1,2,3$, $\cdots, n$. If $p$ is the probability that at least three of the objects occupy places corresponding to their number, then $6 p$ is equal to

The numbers $1,2,3, \ldots, n$ are arranged in a random order. Then, the probability that the digits $1,2,3, \ldots ,k(k < n)$ appears as neighbours, is

A box contains 100 bulbs out of which 10 are defective. A sample of 5 bulbs is drawn. The probability that none is defective, is

Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$. If $P(T)$ denotes the probability of occurrence of the event $T$, then

Two events $\mathrm{E}$ and $\mathrm{F}$ are independent. If $\mathrm{P}(\mathrm{E})=0.3$, $P(E \cup F)=0.5$, then $P(E \mid F)-P(F \mid E)$ equals

If the letters of the word "ATTEMPT" are written down at random then the probability that all the T's are consecutive is

Three different numbers are selected at random from the set $A=\{1,2, \ldots, 10\}$. The probability that the product of two of the numbers is equal to third is

The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.95

There are three bags $X, Y$ and $Z.$ Bag $X$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $Y$ contains 4 one-rupee coins and 5 five-rupee coins and Bag ${Z}$ contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag ${Y},$ is:

A fair die is tossed eight times. The probability that a third six is observed in the eight throw is

A bag contains 5 blue balls and unknown numbers of red balls, two balls are drawn at random. The probability of both of them are blue is $\frac{5}{{14}}$, then the number of red balls are

The probability of India winning a test match against England is $\frac{2}{3}.$ Assuming independence from match to match, the probability that in a 7 match series India's third win occurs at the fifth match, is

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn one-by-one with replacement, then the variance of the number of green balls drawn is

The probability that the same number appear on throwing three dice simultaneously, is

$A$ and $B$ toss a coin alternately on the understanding that the first to obtain head win the toss. The probability that $A$ wins the toss

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :

There are 5 duplicate and 10 original items in an automobile shop and 3 items are brought at random by a customer. The probability that none of the items is duplicate, is