J has 30% chance of winning gold, 40% for silver, 10% for bo

[cab439]

I need some help for this problem.

John has a 30% change of winning a gold medal, 40% chance of winning
silver medal and 10% chance of winning both.

1. What is the probability of winning "at least" 1 medal
2. what is the probability of winning "exactly" 1 medal
3. Given that he wins gold, what is the probability that he wins silver?

 

[pka]

Re: probability help

1) \(\displaystyle P(G \cup S)=P(G)+P(S)-P(G \cap S)\)

2) \(\displaystyle P(G \cap S^c) + P(S \cap G^c)= P(G) + P(S) -2P(G \cap S)\)

3) \(\displaystyle P(S|G)= \frac {P(S \cap G)} {P(G)}\)

 

[cab439]

Re: probability help

Hello - Thanks for the quick reply. I got the solution for 1 and 3.

1. Probability of at least one = 0.3+0.4-0.1 = 0.6

3. Probability of winning silver given gold = 0.1/0.4 = 0.25

I am still not clear on 2. Can you explain?

 

[pka]

Re: probability help

I am still not clear on 2. Can you explain?

Why? You have all the parts. Use them.

Exactly one is \(\displaystyle P(G) + P(S) -2P(G \cap S)\)