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Probability

Long Answer Type

951. A coin is tossed 5 times. X is the number of heads observed. Find the probability distribution of X.

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Short Answer Type

952. Find the probability distribution of X, the number of heads, in the two tosses of a coin (or a simultaneous toss of two coins).

Here X can take the values 0, 1 or 2.

straight P left parenthesis straight X space equals space 0 right parenthesis space equals space straight P left parenthesis no space heads right parenthesis

= P(tails on first loss and tails on the second toss)
= P(tails on first toss) x P(tails on second toss)

equals space 1 half cross times 1 half space equals 1 fourth

P(X = 1) = P(1 head) = P(HT or TH)
= P(HT) + P(TH)

equals space 1 fourth plus 1 fourth space equals space 1 half

P(X = 2) = P(2 heads) = P(HH) =

1 fourth

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Long Answer Type

953. Find the probability distribution of the number of tails when three coins are tossed.

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954. Find the probability distribution of the sum of numbers obtained when two dice are thrown.

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955. Find the probability distribution of the number of times “a total of 9” appears in two draws of two dice.

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Short Answer Type

956. Find the probability distribution of the number of sixes in three tosses of a die.

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957. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of kings.

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958. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of queens.

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959. Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.

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960. Determine the probability distribution of the number of king cards drawn when two cards are drawn one by one without replacement from a pack of 52 cards.

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