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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.

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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.

Let X denote the number of sixes obtained. X takes the values 0, 1, 2, 3.
Probability of 'getting a six' in a single toss of a die =

1 over 6

therefore space space space space straight p space space space straight i. straight e. comma space space space probability space of space success space equals space 1 over 6

q i.e., probability of failure =

1 minus 1 over 6 space equals space 5 over 6

therefore space space space straight P left parenthesis straight X space equals space 0 right parenthesis space equals space straight q space cross times space straight q space cross times space straight q space space equals space 5 over 6 cross times 5 over 6 cross times 5 over 6 space equals space 125 over 216 straight P left parenthesis straight X space equals space 1 right parenthesis space space equals space straight p space cross times space straight q space cross times straight q space plus space straight q space cross times space straight p space space cross times space straight q space plus space straight q space cross times space straight q space cross times space straight p space space space space space space space space space space space space space space space space space space space equals 1 over 6 cross times 5 over 6 cross times 5 over 6 plus 5 over 6 cross times 1 over 6 cross times 5 over 6 plus 5 over 6 cross times 5 over 6 cross times 1 over 6 equals 25 over 216 plus 25 over 216 plus 25 over 216 equals 75 over 216 straight P left parenthesis straight X space equals space 2 right parenthesis space equals space straight p space cross times space straight p space cross times space straight q space plus space straight p space cross times space straight q space cross times straight p space plus space straight q space cross times space straight p space cross times space straight p space space space space space space space space space space space space space space space space space space space equals space 1 over 6 cross times 1 over 6 cross times 5 over 6 plus 1 over 6 cross times 5 over 6 cross times 1 over 6 plus 5 over 6 cross times 1 over 6 cross times 1 over 6 space equals 5 over 216 plus 5 over 216 plus 5 over 216 equals space 15 over 216 straight P left parenthesis straight X space equals space 3 right parenthesis space equals space straight p space cross times space straight p space cross times space straight p space equals space 1 over 6 cross times 1 over 6 cross times 1 over 6 space equals space 1 over 216

∴ probability distribution is

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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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