Question

An urn contains 7 black, 5 red, 8 pink, and 4 orange marbles, if two marbles are picked at random, what is the probability that either both are red or orange?   
1. 9/69
2. 4/81
3. 6/81
4. 4/69
5. 7/65

Answer 1

Correct Answer - Option 4 : 4/69

GIVEN:
Black marbles = 7

Red marbles = 5

Pink marbles = 8

Orange marbles = 4

CONCEPT:

For 'either or' adding function is applied.

FORMULA USED:

P = Number of favorable outcomes/Total number of outcomes

ⁿC_r = n!/r!(n - r)!

CALCULATION:

Way to select two red marbles = ⁵C₂ =10

Way to select 2 orange balls = ⁴C₂ = 6

∴ Required (P) = 10/²⁴C₂ + 6/²⁴C₂

⇒ 16/276 = 4/69

∴ The probability is 4/69.