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Probability

Short Answer Type

991.

Six balls are drawn successively from an urn containing 7 red and 9 black balls. Tell whether or not the trials of drawing balls arc Bernoulli trials when after each drawn the ball drawn is (i) replaced (ii) not replaced in the urn.

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992. There is a group of 10 families each having 5 children of which 2 are boys and 3 are girls. One child is selected from each family, each child of the family being equally likely to be selected. Find the probability that among the 10 children so selected, there are exactly 5 girls.

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993. A pair of dice is thrown 4 times. If a doublet is considered a success, find the probability of 2 successes.

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994. A pair of dice is thrown 10 times. If getting a doublet is considered a success, find the probability of getting 4 successes.

Here n = 10
Let p be the probability that doublet is obtained

$therefore space space space straight p space equals space straight P left curly bracket left parenthesis 1 comma space 1 right parenthesis comma space left parenthesis 2 comma space 2 right parenthesis comma space left parenthesis 3 comma space 3 right parenthesis comma space left parenthesis 4 comma space 4 right parenthesis comma space left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 6 comma space 6 right parenthesis right curly bracket space space space space space space space space space space equals 6 over 36 space equals space 1 over 6 straight q space equals space 1 minus space straight p space equals space 1 minus 1 over 6 space equals space 5 over 6$
Required probability = P(4) = $straight C presuperscript 10 subscript 4 space open parentheses 5 over 6 close parentheses to the power of 6 space open parentheses 1 over 6 close parentheses to the power of 4$

$equals space fraction numerator 10 space cross times space 9 space cross times space 8 space cross times space 7 over denominator 1 space cross times 2 space cross times 3 space cross times 4 end fraction cross times 5 to the power of 6 over 6 to the power of 6 cross times 1 over 6 to the power of 4 space equals 3281250 over 6 to the power of 10$

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995. A box contains 100 tickets each bearing one of the numbers from 1 to 100. If 5 tickets are drawn successively with replacement from the box, find the probability that all the tickets bear numbers divisible by 10.

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Long Answer Type

996. A bag contains 5 white, 7 red and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that
i) none is white? (ii) all are white? (iii) only 2 are white? (iv) at least one is white?

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997.

Five cards are drawn successively with replacement from a well shuffled deck of 52 cards. What is the probability that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is a spade?

94 Views