Question

please help

Sara draws the 9 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card. a. Determine the probability that the second card is another 9. P(9 | 9 of hearts) = Preview b. Determine the probability that the second card is another heart. P(heart|9 of hearts) = Preview c. Determine the probability that the second card is a club. P(club9 of hearts) = Preview d. Determine the probability that the second card is a 7. P(7 9 of hearts) = Preview Write your answers as reduced fractions.

Answer 1

P(A|B) is the conditional probability of Event A which gives us the probability of Event A occuring given that Event B has already occured .

After the first card is drawn , things that have changed from a regular deck of card are :

Since there is no replacement , so the no. of cards total left = 51

No. of number 9 cards left = 4-1 =3 ( since there are total 4 cards of each number )

No. of cards of heart suit left = 13 -1 =12 ( since each suit has 13 cards each)

rest of cards are same as a regular deck of cards

In general , Probability of a Event = No. of favourable outcomes / Total No. of outcomes

a. P( 9| 9 of hearts) = No. of number 9 cards left / Total cards left = 3/51 = 1/17

b. P(heart | 9 of hearts ) = No. of hearts cards left / Total cards left = 12 / 51 = 4 / 17

c. P(clubs| 9 of hearts) = No. of clubs left / Total cards left = 13 / 51

d. P( 7 | 9 of hearts) = No. of number 7 left / Total cards left = 4 / 51

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