Question

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).

Solution

Here n = 5
p = (Probability of getting 5 or 6) = $1 over 6 plus 1 over 6 space equals 1 third comma space space space straight q space equals space 1 minus 1 third space equals 2 over 3$
$straight P left parenthesis straight x space less or equal than space 4 right parenthesis space equals space 1 minus space left square bracket straight P left parenthesis 5 right parenthesis space plus space straight P left parenthesis 6 right parenthesis right square bracket space equals space 1 minus open square brackets straight C presuperscript 6 subscript 5 space open parentheses 2 over 3 close parentheses space open parentheses 1 third close parentheses to the power of 5 space plus space straight C presuperscript 6 subscript 6 space open parentheses 1 third close parentheses to the power of 6 close square brackets space equals space 1 minus space open square brackets 6 over 1 cross times space 2 over 729 plus 1 space cross times space 1 over 729 close square brackets space equals space 1 minus open parentheses 12 over 729 plus 1 over 729 close parentheses space equals space 1 minus 13 over 729 space equals 716 over 729$

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Probability

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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