Question

A bag contains 7 green towels, 5 blue towels, and 8 red towels. Two towels are drawn randomly. What is the probability that both are blue?

1. 1/29
2. 1/22
3. 1/39
4. 1/19
5. None of these

Answer 1

Correct Answer - Option 4 : 1/19

Given:

Green towel = 7

Blue towel = 5

Red towel = 8

Formula:

Probability (E) = Favourable outcomes/Total possible outcomes

Note: here, Probability denoted by ‘E’

The formula used for combination is –

ⁿC_r = n!/(n – r)! × r!

Here,

n = Sample of items.

r = Items are taken at a time.

Calculation:

Favourable outcomes –

2 (out of 5)

⁵C₂ = 5!/(5 – 2)! × 2!

⇒ 5!/3! × 2!

⇒ 5 × 4 × 3!/3! × 2!

⇒ 5 × 4/2 × 1

⇒ 20/2

⇒ 10

∴ Favourable outcomes will be 10

Total possible outcomes –

2 (out of 20)

²⁰C₂ = 20!/(20 – 2)! × 2!

⇒ 20!/18! × 2!

⇒ 20 × 19 × 18!/18! × 2!

⇒ 20 × 19/2 × 1

⇒ 10 × 19

⇒ 190

∴ Total possible outcomes will be 190

Now,

Probability (E) = Favourable outcomes/Total possible outcomes

Probability (E) = 10/190

⇒ 1/19

∴ The Probability that both are blue will be 1/19