Consider a binomial experiment with n = 7 trials where the probability of success on a single trial is p = 0.35. (round your answers to three decimal places.) (a) find p(r = 0). (b) find p(r ≥ 1) by using the complement rule.

A) If the probability of success on a single trial is 0.35, then the probability of failure in a single trial is 1 - 0.35 = 0.65. Out of the 7 trials, P(r = 0), the probability that there will be 0 successes out of the 7 attempts, is calculated by raising (0.65)^7 = 0.0490.
b) If the result does NOT have zero successes, then we automatically know that there must have been at least 1 successful result (it could be anything from 1 to 7). Therefore if the probability of having 0 successes is 0.0490, then the probability of having at least 1 is 1 - 0.0490 = 0.951.

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