A card is drawn from an ordinary deck. Find these probabilities. 1 Of getting a jack 2 Of getting the 6 of clubs (i.e., a 6 and a club) 3 Of getting a 3 or a diamond 4 Of getting a 3 or a 6

Answer 1

A card is drawn at random from a standard deck. So all 52 cards are equally likely to be drawn.

1. The probability of drawing a jack? Among the 52 cards, four are jacks. So 4/52 = 1/13 is the probability that the card drawn is a jack. Also, all 13 denominations are equally likely.
2. The probability of the drawn card being the 6 of clubs? There is only one 6 of clubs, so that probability is 1/52.
3. The probability that the one drawn card is a 3 or a diamond, including the 3 of diamonds or any other 3 or any other diamond)? There are 13 diamonds, including the 3 of diamonds. And there are 3 3's that are not diamonds. So there are 16 cards that are either 3's or diamonds. 16/52 = 4/13 is the probability of this event of drawing a 3 or a diamond when drawing at random from a standard deck.
4. The probability of drawing a 3 or a 6? There are four 3's and four 6's, so there are 8 cards that are 3's or 6's. 8/52 = 2/13 is the probability of that. Also, let T be the event of drawing a three, and let S be the event of drawing a 6. Then the probability of getting a 3 or a 6 is P(T U S) = 1/13 +1/13 = 2/13 because T and S are mutually exclusive events (both cannot happen when drawing one card), and each of the 13 denominations are equally likely.