# involving the computation of probabilities for Bernoulli trials. (1) At least 7 successes in 10 trials with p = 0.3 (2) At least 4 failures in 8 trials with p = 0.55

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involving the computation of probabilities for Bernoulli trials.

(1) At least 7 successes in 10 trials with p = 0.3

(2) At least 4 failures in 8 trials with p = 0.55

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Step 1

Introduction:

If X ~ Bin (n, p), then X represents the number of successes in n trials with probability of success in each trial being p, and the probability mass function of X is:

p (x) = (nCx) px (1 – p)nx; for x = 0, 1, …, n; 0 < p <1; p (x) is 0 otherwise.

Step 2

Part a:

Here, number of trials is the sample size, n = 10.

The probability of success is, p = 0.3.

Thus, the probability of at least 7 successes in 10 trials with p = 0.3 is:

P (X ≥ 7)

= 1 – P (X < 7)

= 1 – P (X ≤ 6)

≈ 1 – 0.9894 [P (X ≤ 6), using Excel...

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