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The probability of getting a success in a trail is five times that of a failure. The probability of getting at most one success in 5 trails, is

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a

$\frac{25}{6^{5}}$

b

$\frac{26}{6^{5}}$

c

${(\frac{5}{6})}^{5}$

d

$2 {(\frac{5}{6})}^{5}$

answer is B.

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Detailed Solution

Let P be the success and q be the failure
$∴ P = 5 q \Rightarrow P = \frac{5}{6}, q = \frac{1}{6} P (X \leq 1) = P (X = 0) + P (X = 1) = 5 C_{0} {(\frac{1}{6})}^{5} {(\frac{5}{6})}^{0} + 5 C_{1} {(\frac{1}{6})}^{4} {(\frac{5}{6})}^{1} = \frac{26}{6^{5}}$

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