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Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`
Concept: undefined >> undefined
If `P(A) = 6/11, P(B) = 5/11 "and" P(A ∪ B) = 7/11` find
- P(A ∩ B)
- P(A|B)
- P(B|A)
Concept: undefined >> undefined
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Determine P(E|F).
A coin is tossed three times, where
E: head on third toss, F: heads on first two tosses
Concept: undefined >> undefined
Determine P(E|F).
A coin is tossed three times, where
E: at least two heads, F: at most two heads
Concept: undefined >> undefined
Determine P(E|F).
A coin is tossed three times, where
E: at most two tails, F: at least one tail
Concept: undefined >> undefined
Determine P(E|F).
Two coins are tossed once, where
E: tail appears on one coin, F: one coin shows head
Concept: undefined >> undefined
Determine P(E|F).
Two coins are tossed once, where
E: no tail appears, F: no head appears
Concept: undefined >> undefined
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
Concept: undefined >> undefined
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
Concept: undefined >> undefined
A black and a red dice are rolled.
Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
Concept: undefined >> undefined
A black and a red dice are rolled.
Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
Concept: undefined >> undefined
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|F) and P (F|E)
Concept: undefined >> undefined
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|G) and P (G|E)
Concept: undefined >> undefined
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P ((E ∪ F)|G) and P ((E ∩ G)|G)
Concept: undefined >> undefined
An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple-choice question?
Concept: undefined >> undefined
Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.
Concept: undefined >> undefined
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
Concept: undefined >> undefined
If P(A) = `1/2`, P(B) = 0, then P(A|B) is ______.
Concept: undefined >> undefined
A die is tossed thrice. Find the probability of getting an odd number at least once.
Concept: undefined >> undefined
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
- both balls are red.
- first ball is black and second is red.
- one of them is black and other is red.
Concept: undefined >> undefined
