Consider a bowl containing ten balls. Five of the balls are red. Three of the ba

Question

Consider a bowl containing ten balls. Five of the balls are red. Three of the balls are green. Two of the balls are white.

1.) Suppose that the balls are mixed around. One of the balls is randomly selected and removed from the bowl. Then the remaining balls are mixed again and a second ball is removed from the bowl. (This is called sampling without replacement.) Use the counting methods to find the probability that both of the balls that were removed from the bowl are red? You must show your work and use the counting methods to earn credit for this question!

2.) Suppose that the balls are mixed around. One of the balls is randomly selected and then returned to the bowl. Then the ten balls are mixed again and a ball is randomly selected. (This is called sampling with replacement.) Use the counting methods to find the probability that both of the balls that were selected are red? You must show your work and use the counting methods to earn credit for this question.

Explanation / Answer

1)

without replacement

10balls=5 red+ 3 green +2 white

probability that both of the balls that were removed from the bowl are red.

probability of getting first ball red is =5/10

probability of getting second ball red is =4/9   

required probability =(5/10)*(4/10)

=20/90

=2/9 =0.22222

2)

with replacement

  probability of getting first ball red is =5/10

probability of getting second ball red is =5/10

required probability =(5/10)*(5/10)

=25/100

=1/4

=0.25

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