Question

A bag contains 5 red, 4 blue and an unknown number m of green balls. If the probability of getting both the balls green, when two balls are selected at random is `1/7`, find m

Answer 1

The bag contains (4 + 5 + m) = (m + 9) balls.

If two balls are drawn from the bag, n(S) = ^(m+9)C₂

Let G ≡ the event that both balls are green

There are m green balls

∴ 2 green balls can be drawn in ^mC₂ ways.

∴ n(G) =  ^mC₂

It is given that,

P(G) = `1/7`

∴ `("n"("G"))/("n"("S")) = 1/7`

∴ 7^mC₂ = ^(m+9)C₂

∴ `(7"m"("m" - 1))/(1*2) = (("m" + 9)("m" + 8))/(1*2)`

∴ 7m² – 7m = m² + 17m + 72

∴ 6m² – 24m – 72 =0

∴ m² – 4m – 12 =0

∴ (m – 6)(m + 2) = 0

∴ m = 6 or m= – 2

∴ m cannot be negative

∴ m = 6.