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Probability

Short Answer Type

1061. An unbiased coin is tossed six times. Find the probability of obtaining at least 2 heads.

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1062. In a box containing 100 bulbs, 10 are defective. What is the probabilities that out of a sample of 5 bulbs
(i) none is defective (ii) exactly two are defective.

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1063. If “getting a 6” in a throw of an unbiased die is a success and the random variable x denotes the number of successes in five throws of the die, find P (2 < x < 5)

Here n = 5
Let p be the probability of getting 6

$therefore space space space space straight p space equals space 1 over 6 comma space space straight q space equals space 1 minus straight p space equals space 1 minus fraction numerator 1 over denominator 6 space end fraction space equals 5 over 6$

$straight P left parenthesis 2 less than straight x less than 5 right parenthesis space equals space straight P left parenthesis 3 right parenthesis space plus space straight P left parenthesis 4 right parenthesis space equals space straight C presuperscript 5 subscript 3 space open parentheses 5 over 6 close parentheses squared space open parentheses 1 over 6 close parentheses cubed space plus space straight C presuperscript 5 subscript 4 space open parentheses 5 over 6 close parentheses space open parentheses 1 over 6 close parentheses to the power of 4 space equals space open parentheses 1 over 6 close parentheses to the power of 5 space space open square brackets fraction numerator 5 space cross times space 4 over denominator 1 space cross times 2 end fraction cross times 25 plus 5 over 1 cross times 5 over 1 close square brackets space equals space open parentheses 1 over 6 close parentheses to the power of 5 space left parenthesis 250 plus 25 right parenthesis space equals space 275 over 776$

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1064. If “getting a 5 or a 6” in the throw of an unbiased die is a success and the random variable x denotes the number of successes in 6 throws of the die, find P (x ≤ 4).

97 Views

Long Answer Type

1065. A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the dice.

286 Views

Short Answer Type

1066. Eight coins are thrown simultaneously. Find the probability of getting at least six heads.

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Long Answer Type

1067.

A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, what is the probability of
(i) no success? (ii) 6 successes? (iii) at least 6 successes? (iv) at most 6 successes?

128 Views