Question

Retest: ProbabilityFor problems 1-3: Johnny Awesome has three red marbles, two blue marbles, five green marbles, and 7 yellowmarbles in a bag. What is the probability that'Johnny.....3) draws a blue marble, does not replace it, and then draws a green marble?

Answer 1

5/136

Explanation

Events

• A: a blue marble is drawn

,

• B: without replacing the first marble, a green marble is drawn

There are 17 (= 3 + 2 + 5 + 7) marbles in total in the bag. Two of them are blue, then the probability of drawing a blue marble is:

`P(A)=(2)/(17)`

After a blue marble is drawn, 16 marbles are left in the bag. Five of them are green, then the probability of drawing a green marble is:

`P(B)=(5)/(16)`

Finally, the probability of drawing a blue marble and then a green marble without replacement is:

`\begin{gathered} P(A\text{ and }B)=P(A)\cdot P(B) \\ P(A\text{ and }B)=(2)/(17)\cdot(5)/(16) \\ P(A\text{ and }B)=(5)/(136) \end{gathered}`