A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a diamond or club. (b) Compute the probability of randomly selecting a diamond or club or heart. (c) Compute the probability of randomly selecting a three or club.

Ok, in a deck of 52 cards we have:

13 clubs, 13 diamonds, 13 hearts, and 13 spades.

For this problem, we assume that the probability of selecting a card at random is the same for all the cards, so each card has a probability of 1/52 of being selected.

then the probability of drawing a given outcome, is equal to the number of times that the outcome appears in the deck divided the number of cards.

a) probability of randomly selecting a diamond or club.

in the 52 cards deck, we have 13 diamonds and 13 clubs, so the probability of drawing a diamond or a club is equal to:

P = (13 + 13) / 52 = 26/52 = 0.5

b) Compute the probability of randomly selecting a diamond or club or heart.

Same reasoning as before, here we have 13 + 13 + 13 = 39 possible options, so the probability is:

p = 39/52 = 0.75.

c) Compute the probability of randomly selecting a three or club.

we have 13 club cards, and in the deck, each number appears 4 times, so we have 4 cards with a number 3 on them.

But one of those 3's is also a club card, so we already counted it in the 13 club cards, then the number of possible options here is:

13 + 4 - 1 = 13 + 3 = 16

then the probability is:

p = 16/52 = 0.31