Answer:
the probability that both marbles drawn will be red is approximately 0.3538 or 35.38%.
Explanation:
To find the probability that both marbles drawn will be red, you can use the probability formula for independent events:
![\[ P(\text{Both Red}) = P(\text{Red on 1st draw}) * P(\text{Red on 2nd draw}) \]](https://img.qammunity.org/2024/formulas/mathematics/college/6n5cms6mycv7slbcnw41703w0l1n6mrnuh.png)
The probability of drawing a red marble on the first draw is the number of red marbles divided by the total number of marbles:
![\[ P(\text{Red on 1st draw}) = \frac{\text{Number of Red Marbles}}{\text{Total Number of Marbles}} = (8)/(8 + 2 + 3) \]](https://img.qammunity.org/2024/formulas/mathematics/college/x2u4m6smhga25jbhup8ismc4jktqbgekgu.png)
After the first marble is drawn, the total number of marbles is reduced by one. The probability of drawing a red marble on the second draw is then:
![\[ P(\text{Red on 2nd draw}) = \frac{\text{Number of Red Marbles}}{\text{Total Number of Marbles - 1}} \]](https://img.qammunity.org/2024/formulas/mathematics/college/dv1dfl88hqju8to9clzmmn3bj27myo8131.png)
Now, multiply the probabilities for both draws:
![\[ P(\text{Both Red}) = (8)/(13) * (7)/(12) \]](https://img.qammunity.org/2024/formulas/mathematics/college/d0nm1wqnbh7xf8pgg9koplmekhsjv4r4qy.png)
Calculate this expression to find the probability:
![\[ P(\text{Both Red}) \approx 0.3538 \]\\](https://img.qammunity.org/2024/formulas/mathematics/college/yojyr1kbds3odvrv9731tyxxcy64aispm9.png)
So, the probability that both marbles drawn will be red is approximately 0.3538 or 35.38%.