suppose you pick two cards from a standard deck of cards. Find the probability of selecting a red card or a spade

Answer 1

R = red card

S = spade card

Two cards are selected from the standard deck. We have possible choices: RR, RS, SR, and SS. Let's find the probability of each choice and add the probabilities together. The cards are drawn without replacement.

P(RR) = (26/52)*(25/51) = 0.2451

P(RS) = (26/52)*(13/51) = 0.1275

P(SR) = (13/52)*(26/51) = 0.1275

P(SS) = (13/52)*(12/51) = 0.0588

P(RR) + P(RS) + P(SR) + P(SS) = 0.2451 + 0.1275 + 0.1275 + 0.0588 = 0.5589

We will be looking for two cards that have either characteristic: red or spade.

P(RS) + P(SR) = 0.255 since order doesn't matter.

P(red or spade) = 0.255/0.5589 = 0.4563

The probability of selecting a red card or a spade is 0.4563.

Answer 2

26 red cards and 13 spades, each of which are black cards

so 39/52 = 3/4