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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.

Here n = 4
Let p be the probability that doublet is obtained
$therefore space space straight p space equals space straight P open curly brackets left parenthesis 1 comma space 1 right parenthesis comma space left parenthesis 2 comma space 2 right parenthesis comma space left parenthesis 3 comma space 3 right parenthesis comma space left parenthesis 4 comma space 4 right parenthesis comma space left parenthesis 5 comma space 5 right parenthesis comma space left parenthesis 6 comma space 6 right parenthesis close curly brackets space equals space 6 over 36 equals 1 over 6 therefore space space space space straight q space equals space 1 space minus space straight p space equals space 1 space minus space 1 over 6 space equals 5 over 6 Required space probability space space equals space straight P left parenthesis 2 right parenthesis space equals space straight C presuperscript 4 subscript 2 space open parentheses 5 over 6 close parentheses squared space open parentheses 1 over 6 close parentheses squared space equals space fraction numerator 4 space cross times space 3 over denominator 1 cross times 2 end fraction cross times 25 over 36 space equals 25 over 216$

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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.

120 Views

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.

139 Views

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?

88 Views

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