Question

In: Statistics and Probability

Two buckets are lying on a table. Bucket #1 has five red and two yellow balls...

Two buckets are lying on a table. Bucket #1 has five red and two yellow balls in it. Bucket #2 contains three red and four yellow balls. In all of the questions below, the buckets start with this composition.

a. Two balls are drawn at random from bucket #1. What is the probability that one is red and one is yellow?

b. One ball is drawn at random from bucket #1 and placed into bucket #2. One ball is then drawn from bucket #2. What is the probability that this ball is red?

c. Balls are drawn one by one from bucket #2 until a red ball is drawn. What is the probability that the first red ball is drawn on the third draw.

Solutions

Expert Solution


Related Solutions

A bucket contains three red balls and four white balls. Two balls are drawn from the...
A bucket contains three red balls and four white balls. Two balls are drawn from the bucket in succession without replacement. What is the probability of getting two white balls, ie. a white ball on the first draw followed by a white ball on the second draw?
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen...
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events, and use them to find the conditional probabilities below. A:{A:{ One of the balls is yellow }} B:{B:{ At least one ball is red }} C:{C:{ Both balls are green }} D:{D:{ Both balls are of the same color }} a) P(B¯¯¯¯|A)= b) P(B¯¯¯¯|D)= c) P(C|D)= Suppose that E and F are events in the sample space with...
In an urn, there are 5 red balls, 5 green balls, 4 yellow balls, and 6...
In an urn, there are 5 red balls, 5 green balls, 4 yellow balls, and 6 white balls. You are drawing balls without replacement. a. When you draw the first ball, what is the probability that the ball will be white? b. Let us assume that you have drawn two balls and both of them are green. What is the probability that the next ball drawn will be green? c. Let us assume that the third ball drawn is also...
An urn contains 5 red balls, 4 green balls and 4 yellow balls, for a total...
An urn contains 5 red balls, 4 green balls and 4 yellow balls, for a total of 13 balls. if five balls are randomly selected without replacement, what is the probability of selecting at least two red balls, given that at least one yellow ball is selected?
1. Suppose that you have ten cards. Five are red, three are yellow and two are...
1. Suppose that you have ten cards. Five are red, three are yellow and two are blue. The five red cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The two blue cards are numbered 1 and 3. The cards are well shuffled. You randomly draw one card. Let R be the event that the card drawn is red and O be the event that the card drawn is odd-numbered....
A box contains 4 red balls, 3 yellow balls, and 3 green balls. You will reach...
A box contains 4 red balls, 3 yellow balls, and 3 green balls. You will reach into the box and blindly select a ball, take it out, and then place it to one side. You will then repeat the experiment, without putting the first ball back. Calculate the probability that the two balls you selected include a yellow one and a green one. 3. Consider a binomially distributed random variable constructed from a series of 8 trials with a 60%...
Consider an urn containing 3 red balls, 5 yellow balls, 7 blue balls, and 6 violet...
Consider an urn containing 3 red balls, 5 yellow balls, 7 blue balls, and 6 violet balls. If 4 balls are drawn at random, what is the probability of drawing one of each color? Suppose we draw 8 balls from the urn above. What is the conditional probability that 4 of them are blue with respect to the event that none of them are yellow?
Conditional Probability Problem: An urn contains 5 red balls, 4 green balls, and 4 yellow balls...
Conditional Probability Problem: An urn contains 5 red balls, 4 green balls, and 4 yellow balls for a total of 13 balls. If 5 balls are randomly selected without replacement what is the probability of selecting at least two red balls given that at least one yellow ball is selected? a) 0.59 b) 0.61 c) 0.63 d) 0.65 e) 0.67
(Urn Poker) An urn contains 8 red balls numbered 1 through 8, 8 yellow balls numbered...
(Urn Poker) An urn contains 8 red balls numbered 1 through 8, 8 yellow balls numbered 1 through 8, 8 green balls numbered 1 through 8, and 8 black balls numbered 1 through 8. If 4 balls are randomly selected, find the probability of getting: three of a kind. (Three of a kind is 3 balls of one denomination and a fourth ball of a different denomination. e.g., 5,5,5,2) (c) two pairs. (A pair is two balls of the same...
An urn contains 4 green balls, five blue balls, and seven red balls. You remove five...
An urn contains 4 green balls, five blue balls, and seven red balls. You remove five balls at random without replacement. Let X be the random variable that counts the number of green balls in your sample. a) Find the probability mass function p(x) describing the distribution of X. b) Find the mean and variance of X
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT