SOLUTION: Suppose a math class contains 33 students, 19 females (three of whom speak French) and 14 males (three of whom speak French). Compute the probability that a randomly selected stude

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Question 1010051: Suppose a math class contains 33 students, 19 females (three of whom speak French) and 14 males (three of whom speak French). Compute the probability that a randomly selected student is female, given that the student speaks French.
Answer by Edwin McCravy(20060) (Show Source):
You can put this solution on YOUR website!
Question 1008795

We make this chart: | MALE |FEMALE|TOTALS| -------------------------------------| Speak French | | | | -------------------------------------| Don't speak it | | | | -------------------------------------| TOTALS | | | | -------------------------------------|

>>Suppose a math class contains 33 students,<<

So we put 33 in the lower right had corner under total. | MALE |FEMALE|TOTALS| -------------------------------------| Speak French | | | | -------------------------------------| Don't speak it | | | | -------------------------------------| TOTALS | | | 33 | -------------------------------------|

19 females (three of whom speak French)

So we put 19 in the total females and 3 in the box under Females that speak French | MALE |FEMALE|TOTALS| -------------------------------------| Speak French | | 3 | | -------------------------------------| Don't speak it | | | | -------------------------------------| TOTALS | | 19 | 33 | -------------------------------------|

>>and 14 males (three of whom speak French)<<

So we put 14 in the total males and 3 in the box under Males that speak French | MALE |FEMALE|TOTALS| -------------------------------------| Speak French | 3 | 3 | | -------------------------------------| Don't speak it | | | | -------------------------------------| TOTALS | 14 | 19 | 33 | -------------------------------------| Now we can fill in the rest of the chart: We add 3+3 and get 6 and put that in the upper right box for the total who speak French. We subtract 14-3 = 11 and put for the Males who don't speak French. We subtract 18-3 = 16 and put for the Females who don't speak French. | MALE |FEMALE|TOTALS| *** -------------------------------------| Speak French | 3 | 3 | 6 | -------------------------------------| Don't speak it | 11 | 16 | | -------------------------------------| TOTALS | 14 | 19 | 33 | -------------------------------------| Now we fill in the total who don't speak French by either adding 11+16=27, or by subtracting 6 who speak French from the 33 total, getting 33=6=27. This is a check that we've done everything correctly. | MALE |FEMALE|TOTALS| -------------------------------------| Speak French | 3 | 3 | 6 | -------------------------------------| Don't speak it | 11 | 16 | 27 | -------------------------------------| TOTALS | 14 | 19 | 33 | -------------------------------------|

Compute the probability that a randomly selected student
is female, given that the student speaks French.

Since we are given that the student speaks French we reduce the sample space to just the top row, eliminating all the ones who don't speak French: | MALE |FEMALE|TOTALS| -------------------------------------| Speak French | 3 | 3 | 6 | -------------------------------------| That's 3 out of 6 or which reduces to . Heck, we could have answered that up there where the 3 stars *** are. We didn't need to even finish filling in the chart. Edwin