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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).

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Long Answer Type

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

Here X denotes the number of tails obtained in three tosses of a coin. Thus X can take the values 0, 1, 2, 3.
Let p be the probability of getting tail and q be the probability of not getting a tail.
$therefore space space space space straight p space equals space 1 half comma space space space straight q space equals space 1 minus space straight p space equals space 1 space minus space 1 half space equals space 1 half straight P left parenthesis straight X space equals space 0 right parenthesis space equals space straight q space straight q space straight q space space equals space 1 half cross times 1 half cross times 1 half space equals space 1 over 8 straight P left parenthesis straight X space equals space 1 right parenthesis space equals space straight p space straight q space straight q space space plus space straight q space straight p space straight q space plus space straight q space space straight q space straight p space space space space space space space space space space space space space space space space space space equals space 1 half cross times 1 half cross times 1 half plus 1 half cross times 1 half cross times 1 half plus 1 half cross times 1 half cross times 1 half space equals space 1 over 8 plus 1 over 8 plus 1 over 8 equals space 3 over 8 straight P left parenthesis straight X space equals space 2 right parenthesis space equals space straight p space straight p space straight q space plus space straight p space straight q space straight p space space plus space straight q space straight p space space straight p equals space 1 half cross times 1 half cross times 1 half plus 1 half cross times 1 half cross times 1 half plus 1 half cross times 1 half cross times 1 half space equals space 1 over 8 plus 1 over 8 plus 1 over 8 equals space 3 over 8 straight P left parenthesis straight X space equals 3 right parenthesis space equals space straight p space straight p space straight p space equals space 1 half cross times 1 half cross times 1 half space equals 1 over 8 space space space space space space space space space space space space$
∴ probability distribution table is

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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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