Question

A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn from the

bag.
What is the approximate probability that exactly two of the five are blue?

Answer 1

the answer is nothing short of 36%

Answer 2

The approximate probability that exactly two of the five are blue is 0.3641

Explanation:

Step 1

The total marble in the bag are
`(10+15+5+20)=50`

• The probability of drawing red marble is =
  `(10)/(50)`=1/5
• The probability of drawing yellow marble is =
  `(15)/(50)`=3/10
• The probability of drawing green marble is =
  `(5)/(10)`=1/10
• The probability of blue marble is =
  `(20)/(50)`=2/5

Step 2

When five marbles are drawn from the bag, we have to find the probability that exactly two of the five are blue.

=Probability that 2 blue marbles and 3 non blue marbles

Step 3

2 marbles should be drawn out of the 20 blue marbles and 3 non blue marbles out of 30 marbles

No of ways =
`20C2(30C3)`

Total no of ways of drawing 5 marbles =
`50C3`

Probability=
`20C2(30C3)/50C5=190(4060)/2118760=0.3641`

Step 4

The approximate probability that exactly two of the five are blue is 0.3641