Question

A bag contains 5 green, 7 red, and 3 pink balls. If four balls are picked at random. What is the probability that either all four are green or any two of them are red?
1. 151/1292
2. 151/1365
3. 563/1292
4. 593/1365
5. 377/1292

Answer 1

Correct Answer - Option 4 : 593/1365

GIVEN:
Green balls = 5

Red balls = 7

Pink balls = 3

CONCEPT:

For 'or' addition and for 'and' multiplication function is applied.

FORMULA USED:
P = Favorable outcomes/Total outcomes

ⁿC_r = n!/r!(n - r)!

CALCULATION:
Total outcomes = ¹⁵C₄ = 1365

Ways to select 4 green balls = ⁵C₄ = 5

ways to select any 2 red = ⁷C₂ × ⁸C₂ = 21 × 28

⇒ 588

Favorable outcomes = 5 + 588 = 593

Required P = 593/1365

∴ The probability is 593/1365.