Question

Suppose you pick a marble from the bag that contains six blue marbles and nine red marbles. You record the color, put the first marble back, and then you draw a second marble. What is the probability that both marbles drawn are red? A. 1/7 B. 12/35 C. 11/29 D. 17/29 E. 27/70

Answer 1

Answer:
`B.\ (12)/(35)`

Explanation:

Given : The bag that contains six blue marbles and nine red marbles.

Number of red marbles = 9

Total marbles = 6+9=15

Total outcomes : The number of combinations of drawing 2 balls from 15 :-

`^(15)C_2=(15!)/(2!(15-2)!)=105`

Favorable outcomes : The number of combinations of drawing 2 red balls from 9 :-

`^(9)C_2=(9!)/(2!(9-2)!)=36`

Now, the probability that both marbles drawn are red :

`\frac{\text{favorable outcomes}}{\text{Total outcomes }}=(36)/(105)\\\\ =(12)/(35)` [divided numerator and denominator by 3]

hence, the required probability =
`\ (12)/(35)`