## Anita505 2 years ago A card is drawn at random from a standard 52-card deck. Events G and H are: G= the drawn card is black H= the drawn card is divisible by 5 (face cards are not valued) (A)Find P(HIG) (B)Test H and G for independence (A)P(HIG)=

1. kropot72

P(H|G) means the probability of H given G. Given that the drawn card is black, the sample space is 26 cards. There are 4 black cards that are either a 5 or a 10. $P(H|G)=\frac{4}{26}=\frac{2}{13}$

2. kropot72

@Anita505 Are you there?

3. Anita505

yes i am here :)

4. Anita505

Thank you for the help! @kropot72

5. kropot72

You're welcome :)

6. Anita505

however would Test H and G for independence... would it be independent? or dependent?

7. Anita505

oh its independent

8. kropot72

If two events A and B are independent, then the probability of A occurring is unaffected by whether of not B has occurred. Therefore if the events are independent P(A|B) = P(A) In this case we test whether P(H|G) = P(H) There are 8 cards that are 5 or 10 and either black or red. Therefore $P(H)=\frac{8}{52}=\frac{2}{13}$ Have we confirmed that H and G are independent?

9. Anita505

Yes this is independent :) thank you once again for your help! much appreciated!

10. kropot72

Correct! You're welcome :)