Answer:
is the required probability.
Step-by-step explanation:
Total number of Marbles = Blue + Red ![= 3 + 5 = 8](https://tex.z-dn.net/?f=%3D%203%20%2B%205%20%3D%208)
Probability of getting blue ![= \frac{3}{8}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B3%7D%7B8%7D)
Probability of not getting a blue ![=\frac{5}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B8%7D)
To get exactly one blue in two draws, we either get a blue, not blue, or a not blue, blue.
<u>First Draw Blue, Second Draw Not Blue:</u>
1st Draw: ![P(Blue) = \frac{3}{8}](https://tex.z-dn.net/?f=P%28Blue%29%20%3D%20%5Cfrac%7B3%7D%7B8%7D)
2nd Draw:
(since we did not replace the first marble)
To get the probability of the event, since each draw is independent, we multiply both probabilities.
![P(Event)=\frac{3}{8}\cdot \frac{5}{7}=\frac{15}{56}](https://tex.z-dn.net/?f=P%28Event%29%3D%5Cfrac%7B3%7D%7B8%7D%5Ccdot%20%5Cfrac%7B5%7D%7B7%7D%3D%5Cfrac%7B15%7D%7B56%7D)
<u>First Draw Not Blue, Second Draw Not Blue:</u>
1st Draw: ![P(Not\:Blue)=\frac{5}{8}](https://tex.z-dn.net/?f=P%28Not%5C%3ABlue%29%3D%5Cfrac%7B5%7D%7B8%7D)
2nd Draw:
(since we did not replace the first marble)
To get the probability of the event, since each draw is independent, we multiply both probabilities.
![P(Event)=\frac{5}{8}\cdot \frac{3}{7}=\frac{15}{56}](https://tex.z-dn.net/?f=P%28Event%29%3D%5Cfrac%7B5%7D%7B8%7D%5Ccdot%20%5Cfrac%7B3%7D%7B7%7D%3D%5Cfrac%7B15%7D%7B56%7D)
To get the probability of exactly one blue, we add both of the events:
![\frac{15}{56}+\frac{15}{56}=\frac{15}{28}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B56%7D%2B%5Cfrac%7B15%7D%7B56%7D%3D%5Cfrac%7B15%7D%7B28%7D)