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Probability

Long Answer Type

821.

Prove that if E and F are independent events, then so are the events E and F'.

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Short Answer Type

822. If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by 1 - P(A') P(B').

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Multiple Choice Questions

823.

Two events A and B will be independent, if

A and B are mutually exclusive
P(A'B') = [1 - P(A)] [1 - P(B)]
P(A) = P(B)
P(A) = P(B)

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Short Answer Type

824. 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?

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825. 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.

Total number of cards = 52
Number of black cards = 26
Let E and F denote respectively events that first and second balls drawn are black
$therefore space space space space straight P left parenthesis straight E right parenthesis space equals space straight P left parenthesis black space ball space in space first space draw right parenthesis space equals space 26 over 52$
$straight P left parenthesis straight F vertical line straight E right parenthesis space equals space 25 over 51$
Required probability = P(E) P(F|E)

$equals space 26 over 52 cross times 25 over 51 space equals 25 over 102$

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826. An unbiased die is thrown. Find the probability of getting 4, 5 or 6 in the first throw and 1, 2, 3 or 4 in the second throw.

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827. Two dice are thrown. Find the probability of getting an odd number on the first die and a multiple of 3 on the other.

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828. A die is tossed twice. Find, the probability of ‘a number greater than 4’ on each dice.

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829. A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. Find the probability of obtaining two tails.

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830. A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. Find the probability of obtaining head and a number 6.

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