There is a bag full of balls numbered 1 to k. As you reach in to pick one, he notes that they are not all equally likely because of magic: ball 1 is least likely to be chosen, with probability c, where c is some constant. Ball 2 has probability 2c, Ball 3 has probability 3c, . . . , Ball k - 1 has probability (k - 1)c, and Ball k has probability kc. What is the expected value of the ball number you pick? Your answer can't use the constant c but will use k.
Two balls are drawn, without replacement, from a bag containing 13 red balls numbered 1−13 and 4 white balls numbered 14−17. (Enter your probabilities as fractions.) (a) What is the probability that the second ball is red, given that the first ball is white? (b) What is the probability that both balls are even-numbered? (c) What is the probability that the first ball is red and even-numbered and the second ball is even-numbered?
A ball is drawn from a bag containing 13 red balls numbered 1-13 and 3 white balls numbered 14-16. (Enter your probabilities as fractions.) (a) What is the probability that the ball is not even-numbered? (b) What is the probability that the ball is red and even-numbered? (c) What is the probability that the ball is red or even-numbered? (d) What is the probability that the ball is neither red nor even-numbered?
Find the indicated probability. A bag contains 15 balls numbered 1 through 15. What is the probability that a randomly selected ball has an even number? 15
3. An urn contains five white balls numbered from 1 to 5, five red balls numbered from 1 to 5 and five blue balls numbered from 1 to 5. For each of the following questions, please give your answer first in the form that reflects your counting process, and then simplify that to a number. You must include the recipes. No other explanation needed. (a) In how many ways can we choose 4 balls from the urn? (b) in how...
A bag contains 3 red and 1 orange ball. You pick two balls from the bag with replacement. What is the probability that you will get two orange balls?
A bag contains 3 red and 1 orange ball. You pick two balls from the bag with replacement. What is the probability that you will get two orange balls? 1/4 0 1/12 1/16
A bag contains 80 balls numbered 1, . . . , 80. Before the game starts, you choose 10 different numbers from amongst 1, . . . , 80 and write them on a piece of paper. Then 20 balls are selected (without replacement) out of the bag at random. (a) What is the probability that all your numbers are selected? (b) What is the probability that none of your numbers is selected? (c) What is the probability that exactly...
Help with c. Check a and b. Seven balls numbered 1 to 7 are placed in a bag. Some of the balls are grey and some are white, as shown below. A ball will be selected from the bag at random. The 7 possible outcomes are listed in the table below. Note that each outcome has the same probability. Complete parts (a) through (c). Write the probabilities as fractions. (a) Check the outcomes for each event in the table. Then,...
1a.) A bag has 2 blue and 3 yellow balls. Draw a tree diagram for drawing 2 balls from the bag, without replacement, and then flipping a coin. Be sure to show the outcomes and probability associated with each outcome. b.) Consider a success to be getting a yellow ball. Use your tree diagram to complete the following distribution table x P(x) c.) What is the probability of getting at least one yellow ball? Show or discuss two different methods...
1.3-9. An urn contains four balls numbered 1 through 4 The balls are selected one at a time without replacement. A match occurs if the ball numbered m is the mth ball selected. Let the event A, denote a match on the ith draw i 1,2, 3, 4. 3! (a) Show that P(A)for each i 4! 2! (b) Show that P(A, nA,) =-, i 1! (d) Show that the probability of at least one match is (e) Extend this exercise...