probability help

Question

An urn contains 7red and 8 green balls. Four balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 4 balls drawn from the urn are red?

Answer 1

You have a total of 7+8 = 15 balls. Since 7 of them are red, you have a 7/15 chance of drawing a red ball. Likewise, since 8 are green, you have an 8/15 chance of drawing a green ball. Since we replace the ball after each draw, the chance of drawing a red ball again is still 7/15. The draws are independent of one another.

 

Since you're drawing 4 times, the probability of drawing 4 in a row is:

(7/15) * (7/15) * (7/15) * (7/15) = (7/15)⁴

 

The result is your answer.