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A card is drawn at random from a standard 52card 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)=
 one year ago
 one year ago
A card is drawn at random from a standard 52card 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)=
 one year ago
 one year ago

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kropot72Best ResponseYou've already chosen the best response.0
P(HG) 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. \[P(HG)=\frac{4}{26}=\frac{2}{13}\]
 one year ago

kropot72Best ResponseYou've already chosen the best response.0
@Anita505 Are you there?
 one year ago

Anita505Best ResponseYou've already chosen the best response.0
Thank you for the help! @kropot72
 one year ago

Anita505Best ResponseYou've already chosen the best response.0
however would Test H and G for independence... would it be independent? or dependent?
 one year ago

kropot72Best ResponseYou've already chosen the best response.0
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(AB) = P(A) In this case we test whether P(HG) = 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?
 one year ago

Anita505Best ResponseYou've already chosen the best response.0
Yes this is independent :) thank you once again for your help! much appreciated!
 one year ago

kropot72Best ResponseYou've already chosen the best response.0
Correct! You're welcome :)
 one year ago
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