A math class contains 7 females (three of whom speak French and the rest speak only English),and 12 males (two of whom speak French and the rest speak only English).

a) A student in the class is chosen at random. If you're told the student is female, what is the probability that the student can speak French?


b) The first student is "placed" back into the class, and another student is chosen at random. If you're told the student can speak French, what is the probability the student is female?

a) If the person is female, then there would be a 3 in 7 chance they can speak french.

b) If the person can speak french, then there would be a 3 in 5 chance they are female.

Hope this helps.

Example In a group 60 people 27 like cold drinks and 42 like hoh drinks and each person likes ot least are of the two drinks how many like both cold and hot drinks?

a) Ah, a probability question! Let's do some math with a sprinkle of humor. We know that there are 7 females in the class, three of whom speak French. So, if we randomly choose a female student, there are 3 French speakers out of the 7 females. The probability is therefore 3/7.

b) Alright, let's place that first student back in the class and randomly choose another one. This time, we're told that this student can speak French. Now, we know that there are 2 French-speaking males and 3 French-speaking females in the class, making a total of 5 French speakers. Out of these 5 French speakers, 3 are female. That means the probability that this student is female is 3/5. Remember, we're assuming the chosen student can speak French. Good luck!

To find the probabilities in both scenarios, we need to use conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred.

a) To find the probability that a female student can speak French, we need to consider the number of females who speak French.

- 3 females speak French.
- The rest of the females (7 - 3 = 4) speak only English.
- So, there are a total of 3 + 4 = 7 females in the class.

Given that the student is female, we only need to consider the 7 females. Out of these 7, 3 can speak French. Therefore, the probability that a female student can speak French is 3/7.

b) To find the probability that a student who can speak French is female, we need to consider the total number of students who can speak French.

- 3 females speak French.
- 2 males speak French.
- So, there are a total of 3 + 2 = 5 students in the class who can speak French.

Given that the student can speak French, we need to consider the 5 students who can speak French. Out of these 5, 3 are females. Therefore, the probability that a student who can speak French is female is 3/5.

To summarize:
a) The probability that a randomly chosen female student can speak French is 3/7.
b) The probability that a randomly chosen student who can speak French is female is 3/5.

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