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

we are assuming they are independent right?

Answer 2

yeah

Answer 3

every time in 4 trials means \((\frac{1}{10})^4=\frac{1}{10000}=.0001\)

Answer 4

because it has to happen each time, so you multiply the probabilities together

Answer 5

by the same argument "never happens" means \((\frac{9}{10})^4\)

Answer 6

" at least once" is a set up for not never, so \(1-(\frac{9}{10})^4\)

Answer 7

and 4th trial only means not first, not second, not third, but yes on 4th so \[\frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\times \frac{1}{10}=(\frac{9}{10})^3\times \frac{1}{10}\]

Answer 8

then a calculator

Answer 9

thanks thanks!