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Q10. [4 points] A box has 9 balls (3 yellow, 2 red, and 4 blue). You are suppose

ID: 3327122 • Letter: Q

Question

Q10. [4 points] A box has 9 balls (3 yellow, 2 red, and 4 blue). You are supposed to pick balls from that box without seeing the inside. a) You will pick one ball. What is the probability that you pick a red ball? b) You will pick one ball. What is the probability that you pick a red or yellow ball? c) You will pick two balls, one after the other without returning the first one. What is the probability that you pick at least one yellow ball? d) You will pick two balls, one after the other without returning the first one. What is the probability that you pick two balls of the same color?

Explanation / Answer

Solution:

Box has 9 balls which has breakup like

3 Yellow

2 Red

4 Blue balls

Solution(a):

Probability of one red ball = 2c1/2c1 =2/9 = 0.222222 = 22.222%

Solution(b):

Probability of red or yellow ball

Probability of red ball = 2/9 = 0.222

probability of yellow ball = 3/9 = 0.333

Total probability of red or yellow ball = 0.222 + 0.333 = 0.555 = 55.555%

Solution(c):

Probability of atleast one yellow ball out of two balls = probability of first yellow ball and another other ball + probability of both yellow ball + probability of first other ball and other yellow ball = (3/9)*(6/8) + (3/9)*(2/8) + (6/9)*(3/8)

= (18/72)+(6/72)+(18/72) = 42/72 = 0.58333 or 58.333%

Solution(d):

Probability of two balls of same color = probability of two yellow balls + probability of two red balls + probability of two blue balls = (3c2 / 9c2) + (2c2/9c2)+ (4c2/9c2) = (6/72)+(2/72)+(12/72) = 20/72 = 0.27777 = 27.777%