An experiment succeeds thrice as often as it fails. Find the probabili

1.	An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.
Answer» An experiment succeeds thrice as often as it fails. ⇒ p = P(getting success) = and q = P(getting failure) = Here, number of trials = n = 5 By binomial distribution, we have P(X = x) = ⁿC_xq^{n -} ^xp^x, x = 0, 1, 2, ....n P(X = r) = ⁵C_r(3/4)^r(1/4)^{5 - r} Now , P(getting at least 3 success) = P(X = 3) + P(X = 4) + P(X = 5) = ⁵C₃(3/4)³(1/4)² + ⁵C₄(3/4)⁴(1/4)¹ + ⁵C₅(3/4)⁵ = (3/4)³[10 x 1/16 + 15 x 1/16 + 9 x 1/16] = 27/64 x 34/16 = 459/512

An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.

Answer»

An experiment succeeds thrice as often as it fails.

⇒ p = P(getting success) = and

q = P(getting failure) = Here, number of trials = n = 5

By binomial distribution, we have

P(X = x) = ⁿC_xq^{n -} ^xp^x, x = 0, 1, 2, ....n

P(X = r) = ⁵C_r(3/4)^r(1/4)^{5 - r}

Now , P(getting at least 3 success) = P(X = 3) + P(X = 4) + P(X = 5)

= ⁵C₃(3/4)³(1/4)² + ⁵C₄(3/4)⁴(1/4)¹ + ⁵C₅(3/4)⁵

= (3/4)³[10 x 1/16 + 15 x 1/16 + 9 x 1/16] = 27/64 x 34/16 = 459/512

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An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.

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