Question

A container contains 6 white, 8 blue and 4 red marbles. Three marbles are drawn at random from the container. Find the probability that each of them is blue?
1. 5/102
2. 11/102
3. 7/102
4. 7/108
5. 13/102

Answer 1

Correct Answer - Option 3 : 7/102

Given:

A container contains 6 white, 8 blue and 4 red marbles. Three marbles are drawn at random from the container

Concept used:

The classical definition of probability

Formula used:

Probability = Favorable Outcome / Total Outcome

P(E) = n(E)/n(S)

ⁿC_r = n! / r!(n - r)!

ⁿC_r = ⁿC_{(n - r)}

Calculation:

Total number of marbles is 6 + 8 + 4 = 18

Let S be the sample space

n(S) = Total number of ways of drawing 3 marbles out of 18 = ¹⁸C₃

Let E = Event of drawing 3 marbles, all of them are blue

n(E) = Number of ways of drawing 3 marbles, all of them are blue

Number of ways of drawing 3 marbles from the total 8 = ⁸C₃

P(E) = n(E) / n(S)

⇒ ⁸C₃/¹⁸C₃

⇒ {(8 × 7 × 6)/(1 × 2 × 3)}/{(18 × 17 × 16)/(1 × 2 × 3)}

⇒ 56/816

⇒ 7/102

∴ The probability that all of them are blue is 7/102.