checking my answers !! please have a look!!

problem 1:

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

of drawing

(a) a king of spades?

(b) a king?

(c) not a king?

(d) a diamond?

(e) a face card (jack, queen, or king)?

answer :

a) 1/52

b)4/52

c)48/52

d)12/52

c)12/52

second problem :

It is believed that 2 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 only gene A, only

gene B or both.

answer :

i said if 67 patients don't have neither A or B, implies that 33 have wether A or B, and we know that 33 patient has gene B and 17 has A, which means the ones who only have gene B is 33-17=16. also 0 patients have only gene A. and then 17 has has 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!!