6. Suppose you have a jar that contains 20 red marbles and 30 black marbles. If

Question

6. Suppose you have a jar that contains 20 red marbles and 30 black marbles. If you randomly sample 2 marbles from this jar (without replacement), what is the probability that you will obtain one of each color?

7. Suppose you have two jars of marbles, each of which contains 20 red marbles and 30 black marbles. If you randomly sample one marble from each jar, what is the probability that you will obtain one marble of each color?

8. If you roll two fair dice, what is the probability of getting: (a) A one and a six?
(b) two numbers that sum to ten?

Explanation / Answer

6)P(obtain one of each color) =P(first one is red and second is black+first one is black and second is red)

=(20/50)*(30/49)+(30/50)*(20/49)=0.4898

7)

P(obtain one of each color) =P(first one is red and second is black+first one is black and second is red)

=(20/50)*(30/50)+(30/50)*(20/50)=0.48

8)as there are total 6*6 =36 outcomes

a)probability of getting a one and a six =2/36=1/18 ( there are 2 outcomes (1,6) ; (6,1))

b) P( two numbers that sum to ten) =3/36=1/12 (3 outcome (4,6),(5,5),(6,4))

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