Determine $P(E|F)$. Two coins are tossed once, where (ii) E : no tail appears, F : no head appears

Compute $P(A|B)$, if $P(B) = 0.5$ and $P(A \cap B) = 0.32$

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

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 ?

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (ii) first ball is black and second is red.

Let A and B be independent events with $P(A) = 0.3$ and $P(B) = 0.4$. Find (i) $P(A \cap B)$

Suppose we have four boxes A,B,C and D containing coloured marbles as given below: 

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

If $P(A) = 0.8$, $P(B) = 0.5$ and $P(B|A) = 0.4$, find (ii) $P(A|B)$

Given two independent events A and B such that $P(A) = 0.3$, $P(B) = 0.6$. Find (ii) P(A and not B)

If $P(A) = \frac{3}{5}$ and $P(B) = \frac{1}{5}$, find $P(A \cap B)$ if A and B are independent events.

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability $\frac{1}{2}$).

Determine $P(E|F)$. A die is thrown three times, E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

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 ? (iii) E : ‘the card drawn is a king or queen’, F : ‘the card drawn is a queen or jack’.

Given two independent events A and B such that $P(A) = 0.3$, $P(B) = 0.6$. Find (i) P(A and B)

Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

If $P(A) = \frac{1}{2}$, $P(B) = 0$, then $P(A|B)$ is

If $P(A) = 0.8$, $P(B) = 0.5$ and $P(B|A) = 0.4$, find (i) $P(A \cap B)$

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