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A test was given to a group of students. The grades and feelings about clowns are summarized below A B n Total Likes Clowns 9 6 5 20 Hates Clowns 18 20 10 48 Total 27 26 15 68 If one student is chosen at random from those who took the test, Find the probability that the student likes clowns GIVEN they got a 'B'.A test was given to a group of students. The grades and feelings about coffee are summarized below A B C Total Likes Coffee 4 5 6 15 Hates Coffee 18 10 20 48 Total 22 15 26 63 If one student is chosen at random from those who took the test, Find the probability that the student got a 'C' GIVEN they hate coffee.Ajar contains 8 red marbles, numbered 1 to 8, and 11 blue marbles numbered 1 to 11. a) A marble is chosen at random. If you're told the marble is blue, what is the probability that it has the number 3 on it? D b) The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 1 on it, what is the probability the marble is blue? D Suppose a math class contains 46 students, 22 who do not wear glasses (three of whom speak French) and 24 who do wear glasses (two of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student wears glasses. [3 A poll was taken of 14,100 working adults aged 40-70 to determine their level of education. The participants were classified by generation and by level of education. The results are shown below. Education Level High School or Less 3203 3178 6381 Bachelor's Degree 3064 3605 6669 A person is selected at random. Compute the following probabilities. (a) What is the probability that the selected person is Gen X, given that they have a Master's degree? D (b) What is the probability that the selected person does not have a Master's degree, given that they are Gen X? D (c) What is the probability that the selected person is Gen Y, given that the person has a Bachelor's degree? D (d) What is the probability that the selected person has a Ph.D., given that they are Gen Y? D A basket at a baby shower contains 4 bottles of pink nail polish numbered 1 through 4, and 3 bottles of red nail polish numbered 1 through 3. One bottle is drawn from the basket at random. A = the polish drawn is pink B : the polish drawn is even-numbered Find P(A | B). 02/3 00/2 07/7 04/4 Suppose your top drawer contains different colored socks: 4 are white, 14 are black, 10 are pink, and 6 are blue. All socks in the drawer are loose (unpaired). In the morning, you randomly select two socks, one at a time. Calculate the following probabilities, writing your answer either as a decimal or a fraction. (a) What is the probability that you get a blue pair of socks? D (b) What is the probability that you do not get a blue pair of socks? D (c) What is the probability that you get either a white pair or a blue pair of socks? D (d) What is the probability that you get one black sock and one white sock? D Ajar contains 4 red marbles numbered 1 to 4 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability of the given event. (a) The marble is red (b) The marble is odd-numbered (c) The marble is red or odd-numbered (d) The marble is blue and even-numbered Nina buys a bag of cookies that contains 7 chocolate chip cookies, 9 peanut butter cookies, 6 sugar cookies, and 5 oatmeal cookies. What is the probability that Nina reaches in the bag and randomly selects a sugar cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie? Round your answer to four decimal places. A bag contains 3 gold marbles, 9 silver marbles, and 26 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win 54. If it is silver, you win 52. If it is black, you lose 51. What is your expected value if you play this game? _ A bag contains 1 gold marbles, 7 silver marbles, and 27 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win 54. If it is silver, you win $3. If it is black, you lose 51. What is your expected value if you play this game? _ A ping pong ball is drawn at random from an urn consisting of balls numbered 2 through 10. A player wins 1 dollar if the number on the ball is odd and loses 1 dollar if the number is even. What is the expected value of his winnings? Express your answer in fraction form. C A card is drawn at random from a standard deck of playing cards (no jokers). If it is red, the player wins 1 dollar; if it is black, the player loses 2 dollars. Find the expected value of the game. Express your answer in fraction form. C Tickets for a raffle cost $15. There were 750 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1900 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)? If the Expected Value is negative, be sure to include the sign with the answer. Express the answer rounded to two decimal places. Expected Value = S