1. (Like Ross, 1.7) Two cards are randomly selected from a deck of 52 playing cards. What is the probability that they are both aces? What is the conditional probability that they are both aces, given that they are of different suits?
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A: The answer is attached below,
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A: S={ (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)…
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A: For any event A and the sample space S, the probability can be found as,
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- A box of shoes contains a random mix of shoes that can be either left or right and can also be either red or black. Note: they are not in matched-pairs! The probability of a shoe being both left-footed and black is 0.35. The probability of a shoe being black is 0.59 and the probability of a shoe being right-footed is 0.36. a) a. What is the probability of a shoe being red? b. What is the probability of a shoe being right-footed and black? C. What is the probability of a shoe being right-footed and red? d. What is the probability of a shoe being left-footed and red? b) = c) = d) =There are 7 councilors in the Ames City council. Three of them are female. Suppose they need to select two councilors for a committee. Which expression is computing the probability that if both councilors are selected at random, both will be female? a. None of the other answers is correct. b. 2C3 / 2C7 c. 3/7 d. None of the other answers is correct. e. 3C2 / 7C2 f. 3C2 / 7C3Given the situation, what is the probability that:C. A player will get 3 acesD. 2 players will get 2 acesE. 2 players will get 1 ace each and 1 player will get 2 acesF. Each player gets an ace and a king
- I need help with A, B, C. Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) = 0.2P(A beats C) = 0.4P(B beats C) = 0.7 and that the outcomes of the three matches are independent of one another. (a) What is the probability that A wins both her matches and that B beats C? and What is the probability that A wins both her matches? (b) What is the probability that A loses both her matches? (c) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)Q6. Dr. Lawrence has three boxes. Their contents are Box 1: 2 red balls and 4 white balls Box 2: 4 red balls and 2 white balls Box 3: 3 red balls and 3 white balls First, a box is selected, and then two balls are drawn at random from that box (without replacement). a. What is the probability that the selected both balls are of the same color. b. If the selected balls are of the same color, what is the probability that they are selected from box 2?The chaper is Probability.
- 7. A drawer contains 6 black socks, 4 brown socks, and 2 green socks. Suppose one sock is drawn from the drawer and that it is equally likely that any one of the socks is drawn. Find the probabilities for each of the following: a. The sock is brown b. The sock is either black or green c. The sock is red d. The sock is not blackThere are 40 pairs of gloves in Bills’ glove basket, but the 80 individual gloves are completely mixed up.a. If 20 gloves are randomly selected, find the probability they include Bills’ favorite pair of gloves.b. If 20 gloves are randomly selected, what is the probability that at most one glove from each of the40 pairs will be picked? (Remember, a left glove is different from a right glove.)In a box, there are 6 red balls and 7 blue balls. 2 blue balls are drawn in the first and second draw. Assuming the balls are not returned, what is the probability of getting at least 2 red balls in the next three draws? a. 11/49 b. 2/13 c. 19/33 d. 12/13 show solutions
- You have a bag of fourteen candies; 2 each of purple, green and yellow, and 4 each of pink and red. Calculate the following probabilities. Answer in fractions 2)What is the probability of choosing a purple first,then replacing it back into the Bag, and then choosing a red?a. You are going to choose a number randomly from the set { 3, 4, 5, 6, ... 19, 20). What is the probability that the number will be divisible by 5 given that the number is even? b.In CSE230, there were 2 assignments this semester. The probabilities that you would get full marks in the first and second assignments are 0.32 and 0.41 respectively. Now, if you get full marks in the first assignment that makes your probability of getting full marks in the second assignment as 0.53. What is the probability of getting full marks in the first assignment given that you got full marks in the second assignment?3. All of the morning math classes are filled & Lisa has a decision to take either Mrs. Fowler or Mr. Williams in the afternoon, what is the probability of Lisa taking a Mrs. Fowler or Mr. Williams in the afternoon? 4. Lisa's school counselor informs her all of Mrs. Fowlers classes are filled. The school adds another teacher Mrs. Jackson. She will teach (1ª, 3rd, 5th, and 6th). What is now the probability of getting Mrs. Jackson for math in the morning?