Question

A bag contains 8 red marbles, 2 blue marbles and 3 green marbles. If two marbles are drawn out of the bag, what is the probability that both marbles drawn will be red?

Answer 1

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:

`\[ P(\text{Both Red}) = P(\text{Red on 1st draw}) * P(\text{Red on 2nd draw}) \]`

The probability of drawing a red marble on the first draw is the number of red marbles divided by the total number of marbles:

`\[ P(\text{Red on 1st draw}) = \frac{\text{Number of Red Marbles}}{\text{Total Number of Marbles}} = (8)/(8 + 2 + 3) \]`

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:

`\[ P(\text{Red on 2nd draw}) = \frac{\text{Number of Red Marbles}}{\text{Total Number of Marbles - 1}} \]`

Now, multiply the probabilities for both draws:

`\[ P(\text{Both Red}) = (8)/(13) * (7)/(12) \]`

Calculate this expression to find the probability:

`\[ P(\text{Both Red}) \approx 0.3538 \]\\`

So, the probability that both marbles drawn will be red is approximately 0.3538 or 35.38%.