Question

Find the probability of drawing a card at random from a deck of 52 playing cards as follows: A red card An Ace A diamond card Not a heart card

Answer 1

Answer:

The probability of drawing a red card is 1/2 as half the cards are red.

The probability of drawing an ace is 4/52

The probability of drawing a red ace is 2/52

So we need the sum 1/2 + 4/52 but we have counted red aces in both of these so we need to subtract the probability of drawing a red ace.

So p(draw an ace or a red card) = 4/52 + 26/52 - 2/52 = 28/52.

Exclusive

The probability of drawing a black ace is 2/52

The probability of drawing a red card that is not an ace is 24/52

So the probability of drawing a red card or an ace but not a red ace is 26/52 = 1/2