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)

Solution

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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Probability

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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