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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.

Here X denotes the number of heads obtained in five tosses of a coin. X can take the values 0, 1, 2, 3, 4, 5.
Let p be the probability of getting a head and q be the probability of not getting a head.
$therefore space space space straight p space equals space 1 half comma space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 half space equals 1 half$
$straight P left parenthesis straight X space equals space 0 right parenthesis space equals straight q space straight q space straight q space straight q space straight q space equals space 1 half cross times 1 half cross times 1 half cross times 1 half cross times 1 half equals space 1 over 32 straight P left parenthesis straight X space equals space 1 right parenthesis space equals space straight p space straight q space straight q space straight q space straight q space plus space straight q space straight p space straight q space straight q space straight q space space plus space straight q space straight q space straight p space straight q space straight q space space plus space straight q space straight q space straight q space straight p space straight q space plus space straight q space straight q space straight q space straight q space straight p space space space space space space space space space space space space space space space space space equals space 1 over 32 plus 1 over 32 plus 1 over 32 plus 1 over 32 plus 1 over 32 space equals 5 over 32 straight P left parenthesis straight X space equals space 2 right parenthesis space equals space straight p space straight p space straight q space straight q space straight q space space plus space space.......... space plus space straight q space straight q space straight q space straight p 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 32 plus 1 over 32 plus..... plus 1 over 32 space equals space 10 over 32 straight P left parenthesis straight X space equals space 3 right parenthesis space equals space straight p space straight p space space straight p space straight q space straight q space plus............ plus straight q space straight q space straight p space straight p space straight p space space space space space space space space space space space space space space space space space space space space equals space 1 over 32 plus 1 over 32 plus.... plus 1 over 32 space equals space 10 over 32 straight P left parenthesis straight X space equals space 4 right parenthesis space equals space straight p space straight p space straight p space straight p space straight q space plus space. space... space plus space straight q space straight p space straight p space straight p space straight p space equals space 1 over 32 plus 1 over 32 plus 1 over 32 plus 1 over 32 plus 1 over 32 space equals 5 over 32 straight P left parenthesis straight X space equals space 5 right parenthesis space equals space straight p space straight p space straight p space straight p space straight p space equals space 1 half cross times 1 half cross times 1 half cross times 1 half cross times 1 half cross times 1 half space equals 1 over 32$

∴ probability distribution of X is

100 Views

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).

83 Views

Long Answer Type

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

75 Views

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

74 Views

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.

121 Views

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.

107 Views

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.

122 Views

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.

88 Views