A school has ten volunteers: six boys and four girls, including Neha and Omar…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A school has ten volunteers: six boys and four girls, including Neha and Omar. A committee of four is chosen at random. Find the probability that it has at least one girl, the probability that it has exactly two girls, and the probability that both Neha and Omar are on it. Give each as a decimal to three places.
Need a reminder? The key ideaShow
Count the favourable and the total outcomes in the same style. counts selections and arrangements. A group of objects that must be together is glued into a block and then multiplied by the arrangements inside the block. A round table of people has seatings.
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. All committees. .
Step 2. At least one girl. No girl means all four from the six boys: . So .
Step 3. Exactly two girls. , so .
Step 4. Neha and Omar. The other two members come from people: . So .
Answer: , and .
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