In the game of Pick-A-Ball without replacement, there are 10 colored balls: 5 red, 2 white, and 3 blue. The balls have been placed into a small bucket, and the bucket has been shaken thoroughly. You will be asked to reach into the bucket without looking and select 2 balls. Because the bucket has been shaken thoroughly, you can assume that each individual ball is selected at random with equal likelihood of being chosen.

Now, close your eyes! Reach into the bucket, and pick a ball. (Click the red Pick-A-Ball! icon to simulate reaching into the bucket and drawing your ball.)

a) What is the probability of selecting the color of ball that you just selected? (Round your answer to four decimal places.)

Don't put your first ball back into the bucket. Now reach in ( again no peeking ), and pick your second ball. ( Click the red Pick-A-Ball icon to simulate reaching into the bucket and select your next ball.)

b) What is the probability of selecting the color of the ball you selected. ( Enter the answer in decimal format to 4 decimal places ).

Answer:

a) the probability of selecting the color of ball ( RED ) that you just selected is 0.5000

b) the probability of selecting the color of the ball ( BLUE ) I selected is 0.3333

Step-by-step explanation:

Given that;

We have a total of 10 colored balls in a small bucket.

Number of Red balls = 5

Number of White balls = 2

Number of blue balls = 3.

Now, assuming I clicked on the red Pick-A-Ball icon to simulate reaching into the bucket and picking a ball.

Also, Assuming that the color of ball that appeared is Red.

Then the probability of selecting the color of ball ( RED ) that I just selected will be;

P( selected Color ) = Number of Red balls / Total number of balls in the bucket

P( selected Color ) = 5 / 10 = 0.5000

Therefore, the probability of selecting the color of ball ( RED ) that I selected is 0.5000

It is said that the game is Pick-A-Ball without replacement.

So assuming I went on and clicked on the red Pick-A-Ball icon to simulate picking a second ball.

Also, Assuming that the color of ball that appeared was blue.

Then the probability of selecting the color of ball ( BLUE ) that I just selected will be;

P( selected Color ) = Number of Blue balls / Total number of balls in the bucket

Now, since I picked the first ball without replacement, i.e I did not return it back to the bucket, The total number of balls left in the bucket now is 9.

so; P( selected Color ) = 3 / 9 = 0.3333

Therefore, the probability of selecting the color of the ball ( BLUE ) I selected is 0.3333

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3 years ago