Suppose that we repeatedly pick a student randomly from the...

Suppose that we repeatedly pick a student randomly from the class to answer a question with replacement (the student can be asked again) from a class of 40 students, 20 of which are male and 20 are female. What is the probability of selecting the second female student before the third male student? [8 points]

Transcript

00:01 Here first let's consider here the probability the probability of selecting selecting a female student a female student on any given trial on any given trial given trial.

00:30 Here since there are 20 female students out of 40, the probability here, the probability of selecting, of selecting a female student, a female student here that is equal to 20 divided by 40 and here that is equal to 1 divided by 2.

00:54 Now let's define the events here that is the f that is the selecting a female student.

01:00 Selecting a female student a female student and here the m that is the selecting a male student selecting a male student male student now here we want to find the probability of selecting second female student before third male student here we have to find the probability of selecting selecting second female student female student before third male student before third male student male student sure this means we are looking for sure that is ffmn or that is we can write fffm for f representing selecting female student m representing the selecting male student now we can break this down into the two cases here and that is ff mm and share that is ff and so here first case there is a effort panel sf and here the probability of being s probability the probability of the first trail of the first trial being similar for a here that is equal to share 1 divided by 2 now here the probability the probability of the second trial the second trial being f sure that is 1 divided by 2 now here the probability of of the third trial the third trial being here that is and here that is one by two and here the probability of the fourth trial being and here that is also one by two so here in in this case, the probability here that is equal to 1 by 2 into 1 by 2 into 1 by 2 into 1 by 2 and here that is equal to 1 divided by 16.

03:48 Now here the second case.

03:51 Here the second case here that is f f f m and here in this case the probability here here the probability of the first trial being f here that is 1 by 2.

04:06 The probability of second trial.

04:13 Second trial being f here that is 1 divided by 2...

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