please check ans: drawing cards / prevelence of genes

problem 1: A card is drawn at random from a standard deck of 52 cards. What is the probability of drawing:

(a) the king of spades?
(b) a king?
(c) not a king?
(d) a diamond?
(e) a face card (jack, queen, or king)?

answers:

a) 1/52
b) 4/52
c) 48/52
d) 12/52
c) 12/52

problem 2: It is believed that two genes, genes A and B, may play some part in the susceptibility of an individual to a disease. Of 100 patients investigated, 17 carry gene A, 33 carry gene B, and 67 carry neither. Find the probability that a patient carries:

a) only gene A
b) only gene B
c) both genes

answers:
I said if 67 patients don't have neither A or B, this implies that 33 have either A or B, and we know that 33 patient has gene B and 17 has A, which means the number who only have gene B is 33 - 17 = 16. Also 0 patients have only gene A. Then 17 have both A and B.

conclusion:
probability of patient:
with only gene A is 0
with only B is 16/100
with both is 17/100

thanks a lot in advance!!

1-a) There is only one king of spades, so "1/52" is correct.

1-b) There are four kings, so "4/52" is correct, but the fraction should probably be simplified.

1-c) There are 52 - 4 = 48 cards that are not kings, so "48/52" is correct, but the fraction should probably be simplified.

1-d) There are four of each suit (hearts, diamonds, clubs, and spades). Divide "52" by "4" to find the number of cards that are diamonds.

1-e) There are three "face" cards in each of the four suits, so "12/52" is correct, but the fraction should probably be simplified.

2-a) If 67 carry neither gene, then the 33 that carry B consistute every remaining patient, and the 17 carrying A are necessarily a subset of those carrying B. Thus, the 17 carrying A also carry B. There are none carrying only A, and "0 probability" is correct.

2-b) Since 17 of the 33 carrying B also carry A, then only 33 - 17 = 16 carry only B. So "16/100" is correct, but the fraction should probably be simplified.

2-c) You already covered this: "17/100" is correct.

Eliz.

thanks very much !! that's so very nice of you !!
good luck with your career!
sincerly,
yassine!