What is the probability of the cars driven out having colour other than yellow? Statement: I) The showroom has 6 white cars, 5 black cars and 4 yellow cars. II)  Three cars are driven out at random.

What is the probability of the cars driven out having colour other than yellow? Statement: I) The showroom has 6 white cars, 5 black cars and 4 yellow cars. II)  Three cars are driven out at random. Correct Answer Both I and II together

Statement: I

Total number of cars = (6 + 5 + 4) = 15

Let, S be the sample space or all possible outcomes.

Then, n(S) = Number of ways of driving 3 cars out of 15

⇒ ¹⁵C3

∵ ⁿCr = n!/r!(n – r)!

⇒ ¹⁵C3 = 15!/3! (15 - 3)!

⇒ 15 × 14 × 13/ 3 × 2 × 1

⇒ 455

Statement: II

Let E = Event of driving out 3 cars, none of which is yellow.

n(E) = Number of ways of drawing 3 cars out of (6 + 5) cars. 

⇒ ¹¹C₃

⇒ 11 × 10 × 9 / 3 × 2 ×1

⇒ 165

From statement I and II

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

⇒ 165/455

⇒ 33/91