Question

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)=

Answer 1

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.
\[P(H|G)=\frac{4}{26}=\frac{2}{13}\]

Answer 2

@Anita505 Are you there?

Answer 3

yes i am here :)

Answer 4

Thank you for the help! @kropot72

Answer 5

You're welcome :)

Answer 6

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

Answer 7

oh its independent

Answer 8

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?

Answer 9

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

Answer 10

Correct! You're welcome :)