A card is drawn at random from a regular deck of 52 cards and is then put back i
ID: 3037018 • Letter: A
Question
A card is drawn at random from a regular deck of 52 cards and is then put back into the deck. A second card is drawn. What is the probability that a. The first card is a club? b. The second card is a heart, given that the first is club? c. The first card is a cub and the second is a heart? d. The first card is an ace and the second is a king? The following table summarizes the graduating class of a Midwestern university: A student is selected at random from the graduating class. Find the probability that the student: a. is receiving a Business degree and is not male. b. is a female, given that the student is receiving an education degree. c. receiving an arts and sciences degree, given that the student is a male. d. is a female, given that the student is receiving an arts and sciences degree or an education degree.Explanation / Answer
4. There are 52 cards in a regular deck of which clubs, heart, spades and diamonds are 13 each.
a. The probability that the 1st card drawn randomly from the deck is a club is 13/52 = ¼ = 0.25.
b. The probability that the 2nd card drawn randomly from the deck is a heart is again 13/52 = ¼ = 0.25, as the 1st card , which was a club, has been put back before drawing the 2nd card, so that the deck had 52 cards, before the 2nd card was drawn randomly.
c. The probability that the 1st card is a club and the 2nd card is a heart is P(A) *P(B) = 0.25*0.25 = 0.0625.
d. The probability that the 1st card drawn randomly from the deck is an ace is 4/52 = 1/13 = 0.076923 (approximately) ( as there are 4 aces in the deck). Since the 1st card has been put back before the 2nd card is drawn, the probability that the 2nd card drawn randomly from the deck is a king is 4/52 = 1/13 = 0.076923. Then, the probability that the 1st card is an ace and the 2nd card is a king is P(A) *P(B)= (1/13)*(1/13) = 1/169 = 0.00591716(approximately).
9. (a).The number of female students receiving a Business degree is 144. There are a total of 2018 students in the class. Hence the probability that a student selected randomly from the class is receiving a Business degree and is not a male is 144/2018 = 0.07136 (approximately).
(b). The number of female students receiving an Education degree is 102. Hence the probability that a student selected randomly from the class is receiving an Education degree and is Female is 102/2018 = 0.00505(approximately).
(c ) The number of male students receiving an Arts and Science degree is 342.Hence, the probability that a student selected randomly from the class is receiving an Arts and Science degree and is a male is 342/2018 = 0.16947 (approximately).
(d) The number of female students receiving an Arts and Science degree is 324. Also, the number of female students receiving an education degree is 102. Therefore, the probability that a student selected randomly from the class is receiving an Arts and Science degree or an Education degree and is a female is (324+102)/2018 = 426/2018 = 0.2111 (approximately).
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