old_dream_1976 wrote:

What is the probability of getting two cards belonging to two different suits when two cards are drawn at random from a pack of well shuffled cards comprising 52 cards?

a)1/13

b)13/17

c)13/51

d)26/51

e)7/13

how do you figure out that the two cards are drawn one after the other or simultaneously ?

the answers differ based on the assumption one makes.

Lets solve it first for the case where the card is replaced:

For any one of the 4 types, P of getting the same type = 1/4 * 1/4 = 1/16.

since there are 4 card types, p = 4 * 1/16 = 1/4. Therefore, P of not getting the same type (which is what we want) is 1 -1/4 = 3/4.

Lets now solve it for the case where the card is not replaced.

P of the same card type (for each card type)= 1/4 * 12/51 = 1/17

Since there are 4 card types, P = 4 * 1/17 = 4/17

Thus, P that this is not the case = 1 -14/17 = 3/17, hence B