Question

A bag contains 6 blue, 8 red and 11 green marbles. What is the probability that ablue marble is pulled from the bag, replaced and then a green marble is pulled fromthe bag?A. 0.25B. 0.17C. 0.66D. 0.11

Answer 1

D. 0.11

Step-by-step explanation

When the first marble is pulled, there is a total of 25 marbles in the bag, 6 of which are blue. So the probability of drawing a blue marble the first time is,

`P(blue)=(6)/(25)`

Then, that marble is put back in the bag, so we still have 25 marbles in the bag. 11 of which are green, so the probability of drawing a green marble the second time is,

`P(green)=(11)/(25)`

The probability that the first marble is blue and the second marble is green, if the first one is replaced, is,

`P(B_(1st)G_(2nd))=P(blue)\cdot P(green)=(6)/(25)\cdot(11)/(25)=(66)/(625)=0.1056\approx0.11`

Hence, the probability that a blue marble is drawn, put back, and then a green marble is drawn is 0.11.