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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)

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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).

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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.

A die is thrown again and again.
Probability of getting a six in a throw =

1 over 6

Probability of not getting a six in a throw =

1 minus 1 over 6 space equals 5 over 6

Since third six is in sixth throw
∴ there are two sixes in first five throws and one six in the sixth throw.
Probability of getting two sixes in 5 throws =

straight C presuperscript 5 subscript 2 space open parentheses 5 over 6 close parentheses cubed space open parentheses 1 over 6 close parentheses squared

open square brackets because space space space straight n space equals space 5 comma space space space straight p space equals space 1 over 6 comma space space straight q space equals space 5 over 6 close square brackets

Probability of getting a six in sixth throw =

1 over 6

∴ probability of getting a third six in the sixth throw

equals space straight C presuperscript 5 subscript 2 space open parentheses 5 over 6 close parentheses cubed space open parentheses 1 over 6 close parentheses squared space cross times space 1 over 6 space equals space fraction numerator 5 space cross times space 4 over denominator 1 space cross times 2 end fraction cross times 125 over 6 to the power of 6 space equals 1250 over 46656 space equals 625 over 23328.

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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?

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