a. A bag contains 2 red and 5 green balls. We draw 4 balls from the bag with rep

Question

a. A bag contains 2 red and 5 green balls. We draw 4 balls from the bag with replace- ment. Find the probability that we did not get a red ball until the last draw. b.. A jar contains 3 red marbles, 7 green marbles and 10 white marbles. A marble is drawn from the jar at random, put back into the jar, and then a second marble is picked. What is the probability that both marbles picked are white? c. If you roll a pair of fair dice, find the probability that the product of the two numbers you rolled is a prime number.

Explanation / Answer

Solution:-

a. A bag contains 2 red and 5 green balls. We draw 4 balls from the bag with replace- ment. Find the probability that we did not get a red ball until the last draw.

Probability of getting Red ball = 2/7

Probability of getting Green ball = 5/7

P(a red ball until the last draw) = 5/7 * 5/7 * 5/7 * 2/7 = 0.10412328196 or 0.1041

b.. A jar contains 3 red marbles, 7 green marbles and 10 white marbles. A marble is drawn from the jar at random, put back into the jar, and then a second marble is picked. What is the probability that both marbles picked are white?

Probability of Red marble = 3/20

Probability of green marble = 7/20

Probability of white marble = 10/20

P(both marbles picked are white) = 10/20 * 10/20 = 0.25

c. If you roll a pair of fair dice, find the probability that the product of the two numbers you rolled is a prime number.

Sample space of rolling a pair of fair dice = {(1,1), (1,2), (1,3), ..... (6,5), (6,6)}

P( the product of the two numbers you rolled is a prime number) = P(A)?

Sample space of such numbers = {(1,2),(2,1),(1,3),(3,1),(1,5),(5,1)}

P(A) = 6/36 = 1/6

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.