Answer to question 7

We are given that P(`success') = .05, on each `experiment' individually. We first want to find P(exactly one success in 10 repetitions of the experiment). This is found via the multiplication rule and the addition rule for probabilities.

First, the multiplication rule gives us the probability of, say, a `success' on trial #1 and failures on all the others, namely

Now the addition rule gives us the probability of (`success' on trial #1 only, or `success' on trial #2 only, or ...)

which is the probability we're looking for.

P(at least one success) = 1 - P(no successes in 10 trials), and by the multiplication rule

So our answer is .

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