Basic problems on Probability

Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4, find P (E|F) and P(F|E)

A die is thrown twice and the sum of the numbers appearing is observed to be 6. find the conditional probability that the number 4 has appeared at least once?

A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.

Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?

If P (A) = 0.18, P (B) = 0.5 and P (B|A) = 0.2, find P(A n B)?

If P(A) = 5/13, P(B) = 7/13, and P(A ∩ B) = 8/13, Find P(A ∪ B)?

An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?

If P(A) = 6/17, P(B) = 5/17, and P(A ∪ B) = 4/17 Find P(B|A)?

If P(A) = 2/15, P(B) = 4/15, and P(A ∪ B) = 6/15 Find P(A|B)

Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are queens and the third card drawn is an ace?

A die is thrown. If G is the event ‘the number appearing is a multiple of 3’ and H be the event ‘the number appearing is even’ then find whether G and H are independent ?

6 Coins are tossed simultaneously. find the probability to get 2 hands

If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.

An unbiased die is thrown twice. Let the event A be ‘odd number on the first throw’ and B the event  ‘odd number on the second throw’. Check the independence of the events A and B.

Let A and B be independent events with P (A) = 0.7 and P(B) = 0.7. Find P(A n B)?

Events A and B are such that P (A) = 1/3, P(B) = 7/6, and P(not A or not B) = 1/4. State whether A and B are independent?

If A and B are two events such that P (A) = 3/4, P (B) = 1/2 and P (A n B) = 3/8, find P (not A and not B).

Let A and B be independent events with P (A) = 0.2 and P(B) = 0.8. Find P(A/B)?

Let A and B be independent events with P (A) = 0.13 and P(B) = 0.3. Find P(B/A)?

The probability of second event in the situation if the first event has been occurred is classified as

The probability which is based on the self-beliefs of the persons involved in the experiment is classified as

The joint probability of the independent events J and K is equal to

Consider two events X and Y, the X-bar and Y-bar represents

The variation in which outcomes of experiments are effected by uncontrolled factors is considered as

If two events X and Y are considered as partially overlapping events then the rule of addition can be written as