probability and counting

1. Sara draws the 33 of hearts from a standard deck of $2 cards. Without replacing the first card, she then proceeds to draw a second card. a. Determine the probability that the second card is another 3. P(3 3 of hearts) = b. Determine the probability that the second card is another heart. PCheart (3 of hearts) = c. Determine the probability that the second card is a club. P(club | 3 of hearts) = d. Determine the probability that the second card is a 10. P(10 | 3 of hearts) = Write your answers as reduced fractions. 2. Amber rolls a 6-sided die. On her first roll, she gets a "1". She rolls again. (a) What is the probability that the second roll is also a "1". P(1 [ 1) = (b) What is the probability that the second roll is a "4". P(4 | 1) = 3. A 6-sided die rolled twice. Let E be the event "the first roll is a 5" and F the event "the second roll is a 5". (a) Are the events E and F independent? Input Yes or No: (b) Find the probability of showing a 5 on both rolls. Write your answer as a reduced fraction. Answer. = 4. Below is a list of all possible outcomes in the experiment of rolling two die. 1, 1 1, 2 1, 3 1,4 1,5 1,6 2, 1 2, 2 2, 3 2,4 2,5 2,6 3, 1 3, 2 3, 3 3,4 3, 5 3,6 4, 1 4, 2 |4,3 4, 4 4, 5 4, 6 5, 1 5,2 5,3 5, 4 5, 5 5, 6 6, 1 6,2 6,3 6,4 6, 5 6,6 Determine the following probabilities. Write your answers as reduced fractions. P(sum is odd) = P(sum is 5) = P(sum is 7) = P(sum is 7 and one of the die is a 1) = P(sum is 7 or one of the die is 1) = 5. A die is rolled twice. What is the probability of showing a 1 on the first roll and an even number on the second roll? Write your answer as a simplified fraction