# Thread: Probability Problem Using General Multiplication Rule

1. ## Probability Problem Using General Multiplication Rule

Would someone please show me how to find P(M1), P(F2), and P(M3) from the problem below

Problem: A company employs six male executives and three female executives. Three executives are randomly selected, one at a time, from the nine executives; the first one selected is sent to China, the second one is sent to New York, and third one is sent to France. Using the general multiplication rule, find the probability that a male is sent to China, a female is sent to New York, and a male is sent to France. Express your answer as a reduced fraction. Hint: Write the probability as P(M1F2M3), then apply the rule.

Here is how I approach the solution:
1. the Sample space S = 9(8)(7) = 504 ways to choose the 3 executives randomly
2. P(M1F2M3) = P(M1)*p(F2|M1)*P(M3|M1F2)
3. But I am not sure how to find P(M1) or P(F2) or P(M3)

2. ## Re: Probability Problem Using General Multiplication Rule

Originally Posted by Mathlv
Problem: A company employs six male executives and three female executives. Three executives are randomly selected, one at a time, from the nine executives; the first one selected is sent to China, the second one is sent to New York, and third one is sent to France. Using the general multiplication rule, find the probability that a male is sent to China, a female is sent to New York, and a male is sent to France. Express your answer as a reduced fraction. Hint: Write the probability as P(M1F2M3), then apply the rule.
$\mathcal{P}(M_3F_2M_1)=\mathcal{P}(M_3|F_2M_1) \mathcal{P}(F_2|M_1)P(M_1)$.

Now, $\mathcal{P}(F_2|M_1)P(M_1)=\frac{3}{8}\cdot\frac{6 }{9}$

Can you finish?

3. ## Re: Probability Problem Using General Multiplication Rule

Thank you very much for the help Plato.
Yes, I think I can finish the rest of the problem.
I hope my P(M3) is correct
P(M3) = 5/7
P(M1F2M3) = P(M1)P(F2|M1)P(M3|M1F2) = 2/3*3/8*5/7 = 30/168 = 5/28

P.S. I really like your math display. You must use Math Type Program or something. I have Math Type but I could not copy and paste on this page. Any idea how I can display my math symbol here? Thanks again.

4. ## Re: Probability Problem Using General Multiplication Rule

Originally Posted by Mathlv
You must use Math Type Program or something. I have Math Type but I could not copy and paste on this page. Any idea how I can display my math symbol here? Thanks again.
[TEX]\mathcal{P}(F_2|M_1)P(M_1)=\frac{3}{8}\cdot\frac{6 }{9}[/TEX] gives $\mathcal{P}(F_2|M_1)P(M_1)=\frac{3}{8}\cdot\frac{6 }{9}$

I just typed that up. It is basic LaTeX.
From MathType just copy the code wrap it in the [TEX]...[/TEX] tags.
Be to remove extra symbols such as  and any linefeeds.

5. ## Re: Probability Problem Using General Multiplication Rule

Thanks again.