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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?

Retest ProbabilityFor problems 13 Johnny Awesome has three red marbles two blue marbles five green marbles and 7 yellowmarbles in a bag What is the probability class=

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Answer

5/136

Step-by-step 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:

[tex]P(A)=\frac{2}{17}[/tex]

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:

[tex]P(B)=\frac{5}{16}[/tex]

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

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

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