Answer to Question #180604 in Statistics and Probability for Agust D

Question

Answer the following, final answer must be reduced to lowest term.

1. The probability of getting even number if a fair die is rolled.
2. The probability of getting hearts in a deck of a card.
3. The probability of getting aces in a deck of card
4. The probability of getting a black cards in a deck of card
5. The probability of getting a 2 head in tossing 3 coins

Answer 1

1. There are 6 possibilities, 3 are odd and 3 are even. So $\frac{3}{6}=$ $\frac{1}{2}$
2. There are 52 cards in the deck, 13 of them are hearts, so $\frac{13}{52}=$ $\frac{1}{4}$
3. There are 52 cards in the deck, 4 of them are aces, so $\frac{4}{52}=$ $\frac{1}{13}$
4. There are 52 cards in the deck, 26 of them are black, so $\frac{26}{52} =$ $\frac{1}{2}$
5. The sample space has size 2³ = 8, and there are 3 possible ways to get 2 heads out of 3 coins (1 and 2, 2 and 3, 1 and 3), so total probability is $\frac{3}{8}$.