Question

HELP PLEASE I DON'T UNDERSTAND

Answer 1

Answer:

Step-by-step explanation:

First thing you need to do is to check if the sample data has also that 40% cycling boys, since the information you are given is not exact is "about 40%".

I did it counting in excel so not to miscount by accident, and the result was 54 numbers bellow 4 and 150 total numbers.

That comes down to 54/150 or 0.36, so in this particular set of data only 36% of the boys commute by cycle.

Now, this gives us a probability of 36% of finding a boy who commutes by bicycle on the first pick, but we want to know the probability of 3 failures and then a success. This is represented by p=0.36 and q=0.64, where q is the probability of failure on the first try.

This means that the event will occur on the first trial with probability p. If that fails, then it will occur on the next trial with a probability of (1−p)p or q*p. If that also fails, then continuing on, the probability of the event happening on the third trial is $(1-p)^{2}p$ or $q^{2} p$.  If we go on and on we can see that the probability of the first success on the nth trial is $(1-p)^{n}p$ or $q^{n}p$. If n=4 then the probability would be:

$P=q^{4}p=0.64^{4} *0.36=0.1678*0.36=0.0604$

P=6.04%

Answer 2

If I counted correctly, the answer would be 52/150. You just need to simplify the fraction. I'll recount soon, and update if it changes.