Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up box holds phones, and of them are faulty. Two phones are picked at random without replacement. Find the probability that both are faulty, the probability that none is faulty and the probability that exactly one is faulty. Give four decimal places.
In a probability tree, multiply along a path and add the paths that make the event. Without replacement, the second branches use the counts that are left. From a big population the draws are almost independent.
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. Both faulty. .
Step 2. None faulty. .
Step 3. Exactly one. .
Answer: , and .
Check. The two paths of exactly one are and . Each is , and together they make .
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