The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ?

Determine $P(E|F)$. Mother, father and son line up at random for a family picture E : son on one end, F : father in middle

A couple has two children, (i) Find the probability that both children are males, if it is known that at least one of the children is male.

In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random. (c) If she reads English newspaper, find the probability that she reads Hindi newspaper.

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (ii) at least one is a girl?

Evaluate $P(A \cup B)$, if $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent ? (i) E : ‘the card drawn is a spade’, F : ‘the card drawn is an ace’

A die is tossed thrice. Find the probability of getting an odd number at least once.

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

If $P(A) = \frac{6}{11}$ , $P(B) = \frac{5}{11}$ and $P(A \cup B) = \frac{7}{11}$, find (i) $P(A\cap B)$

Probability of solving specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that (ii) exactly one of them solves the problem.

Let A and B be independent events with $P(A) = 0.3$ and $P(B) = 0.4$. Find (iv) $P(B|A)$

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl,

There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?

A couple has two children, (ii) Find the probability that both children are females, if it is known that the elder child is a female.

Given that E and F are events such that $P(E) = 0.6$, $P(F) = 0.3$ and $P(E \cap F) = 0.2$, find $P(E|F)$ and $P(F|E)$

Given that the events A and B are such that $P(A) = \frac{1}{2}$, $P(A \cup B) = \frac{3}{5}$ and $P(B) = p$. Find $p$ if they are (ii) independent.

If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?

If $P(A|B) > P(A)$, then which of the following is correct :