1. A scientist performs an experiment 10 times. Each experiment has a 5% chance

Question

1. A scientist performs an experiment 10 times. Each experiment has a 5% chance of failing.

a) What is the probability that at least one of those 10 experiments fails?

b) What is the probability that none of the experiments fail?

c) What is the probability that the first experiment fails?

d) What is the probability that the second experiment fails, given that the first did not?

e) What is the probability that all 10 of the experiments fail?

Please show all work using the computer program R functions dealing with discrete probability distributions.

Explanation / Answer

1. a Probability that at least one of those 10 experiments fails = 1 - probability that no experiments fails = 1 - (0.95)^10.

b. Probability that none of the experiments fail = (0.95) ^10.

c. Probability that the first experiment fails = 0.5 x (0.95) ^9.

d.Probability that all 10 of the experiments fail = 0.5 ^10

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