Question

4. The pair of events that is non-mutually exclusive is A. Turning over an odd number and turning over an even number B. Turning over a prime number and turning over a perfect square C. Turning over a one-digit number and turning over a two-digit number D. Turning over a multiple of 2 and turning over a multiple of 7 5. A student draws one card at random from a standard deck of 52 playing cards. The probability that the card is a diamond or a face card is A. 0.058 B. 0.077 C. 0.423 D. 0.481 Use the following information to answer the next question. On any particular Saturday evening, the probability that Hannah will go 1 to the movies and go for a coffee is The probability that she will go

Answer 1

In one deck we have Spades, Clubs, Hearts, and Diamonds. Each one has 13 cards and 3 face cards. So the let's do this step by step. The probability to get a diamond card is:

$P(diamond)\text{ = }\frac{13}{52}$

(13 diamond cards in a total of 52). Then the probability to get a face card is:

$P(facecard)\text{ = }\frac{12}{52}$

(12 face cards in a total of 52). We have to sum these probabilities but also we have to subtract the possibilities that include a card that is a face card and diamond (because if we don't do that we are going to count these cards two times). This probability is:

$P(DiamondandFaceCard)\text{ = }\frac{3}{52}$

(We have only 3 cards in the deck that are diamond and face cards). Therefore, the probability will be:

$\text{Probability = P(diamond) + P(facecard) - P(Diamond and Face Card)}$$\text{Probability = }\frac{13}{52}\text{ + }\frac{12}{52}\text{ - }\frac{3}{52}$$\text{Probability = }0.423$