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A trial is repeated 6 times, and each trial succeeds with probability 0.4…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A trial is repeated times, and each trial succeeds with probability . How many orders give exactly successes? How many give exactly successes? What is the probability of the one order in which the first two trials succeed and the last four fail? Give the probability to four decimal places.
Need a reminder? The key ideaShow
A count is binomial when there are two outcomes, independent trials, a fixed number of trials and the same chance . One order with successes has probability , and there are orders.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Two successes. .
Step 2. Four successes. Choosing the successes is the same as choosing the failures, so .
Step 3. One order. .
Answer: , and about .
What if? is , because all orders have the same probability.
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