Question

A bag contains two red marbles and five blue marbles. you draw a marble, record its color, replace it, and then draw a second marble. what is the probability that you draw a blue marble at least once?

a.0.28
b.0.49
c.0.71
d.0.92

Answer 1

Answer: d. 0.92

Explanation:

Given : Number of blue marbles in bag = 5

Number of red marbles in the bag = 2

Total marbles in bag= 5+2=7

Since, we draw a marble, record its color, replace it, and then draw a second marble.

It means every outcome is independent of each other.

Now, the probability that you draw a blue marble at least once = 1- P(no blue marble drawn)

=
`1-\text{P(both marble are red)}\\\\=1-(2)/(7)*(2)/(7)\\\\=1-(4)/(49)\\\\=(49-4)/(49)\\\\=(45)/(49)=0.918367346939\approx0.92`

Hence, the probability that you draw a blue marble at least once= 0.92

Hence, the correct answer is d. 0.92 .

Answer 2

2+5 = 5 total marbles

5 are blue so you have a 5/7 chance of picking blue each time

5/7 = 0.714 rounded to 0.71