You rock! Keep up the good work. 😊

Yay! So glad I could help. 😊

Good luck on your test!! I’m glad I could support the cause. Also, I appreciate your feedback. 😎

You’re welcome! 😊

I appreciate your feedback. 😊

I very much appreciate your feedback. 😊

I’m happy to help. 😊

I appreciate your feedback. 😊

🤔😄😜😴

I’m sorry. I don’t know how to do this one. 😔

To solve this problem, we can use the concept of conditional probability. Let's define the events: - Event A: The 10th and last male recipient of free shampoo is also the 35th recipient of free samples. - Event B: Rey gives free shampoo to a male participant. Given: - Total number of participants = 142 (females) + 78 (males) = 220 - Rey stops giving free samples after giving exactly 10 free samples to male participants. We need to find the probability of Event A given Event B has occurred. The probability of Event B (Rey gives free shampoo to a male participant) is the probability of selecting a male participant, which is \( \frac{78}{220} = \frac{39}{110} \). Now, let's calculate the probability of Event A: - The probability that the 10th male recipient of free shampoo is also the 35th recipient is \( \frac{1}{78} \) because there is only one 10th and last male recipient. - The probability that the other 9 male recipients are not the 35th recipient is \( \frac{77}{78} \) for each of them. Therefore, the probability of Event A is: \[ P(A) = \left( \frac{1}{78} ight) \times \left( \frac{77}{78} ight)^9 \] Now, we multiply the probability of Event A by the probability of Event B to get the final answer: \[ P(A \cap B) = P(A) \times P(B) = \left( \frac{1}{78} ight) \times \left( \frac{77}{78} ight)^9 \times \frac{39}{110} \] By calculating this expression, we should arrive at the correct answer of approximately 0.02905.

Here are two situations that sound similar, but are not the same. Situation A: find the probability of randomly selecting a female given that she is French. This is what you are calculating when you do 10/60.Situation B: find the probability of randomly selecting a person who is female and French. This is the situation in the question. Imagine that you have all of the 100 names on cards mixed in a bin. Situation B would be like if your friend pulled out one name at random and sealed it in an envelope and then asked you to calculate the probability that the person in the envelope is female and French (female/100)(French/100). Situation A would be like if your friend pulled a name at random and put it in the envelope and said, “The person in the envelope is French. Calculate the probability that the person in the envelope is female.” Because your are given the additional information that the person is French, you can narrow it down to 60 people who are French and 10 of them are female, so 10/60. In the question in the video, Situation B, you are not told in advance that the person in the envelope is female. You are blind to both gender and nationality, as you calculate the probability that the person in the envelope is female and French, so can’t narrow it down to 60 people, you have to calculate each probability (female, French) using the full 100 and then multiply. This is a tough concept. I hope this explanation helps.

The following two questions are not calculated the same way: 1) What is the probability of selecting a student who is female and French? 2) What is the probability of selecting a female student given that the student is French. In #1 the probability is indeed 10/100 (Target/Total). However, in #2, the statement “given that the student is French” changes the total. We now consider ONLY the French students as the total. The question is now equivalent to asking the probability of selecting a female student out of a group made of only the French students. 10/60 (Target/NewTotal). 😎

@@MrHelpfulNotHurtful thank you

high school