Question

Suppose that an experiment is repeated four times. A certain event has probability 1/10 in a single repetition of the experiment.

What is the probability that the event occurs every time in the 4 trials?
What is the probability that it never occurs?
What is the probability that it occurs at least once?
What is the probability that it occurs in the fourth trial only?

Answer 1

Answers:

1/10,000

6561/10,000

3439/10,000

729/10,000

Explanation:

Plug in (1/10)^4

Answer 2

Best thing you can do in order to answer all of this is to use the Bernoulli trials. You can look for it and see if the answers I'm giving you are correct:
Probability of occurring 4 times = (1/10)^4
Probability of never occurring = (9/10)^4
Probability that it occurs at least once = 1 - (9/10)^4
Probability that it occurs in the fourth trial only = (9/10)^3 * 1/10
I think this is going to be very helpful