Idon't understand

about 40% of the boys in walter’s school commute to school by bicycle. what is the probability that you must select at least four boys to find one boy who commutes by bicycle? use the table of randomly generated numbers to answer the question. the numbers 0 to 3 represent boys who commute to school by bicycle, and the numbers 4 to 9 represent boys who do not commute by bicycle.

003 448 311 790 832 265 843 608 354 736 578 994 968 895 754 660 340 085 622 968 346 353 312 544 167 978 005 371 146 607 323 337 821 617 892 976 985 448 830 409 549 804 464 597 323 147 317 789 915 267

based on this data, the estimated probability that it will take at least four boys to find one who commutes by bicycle is

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 or .  If we go on and on we can see that the probability of the first success on the nth trial is or . If n=4 then the probability would be:

P=6.04%

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step-by-step explanation: