A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that

Given: A bag containing 7 white, 5 black and 4 red balls.

By using the formula,

P (E) = \( \dfrac{favourable\; outcomes }{total\; possible\; outcomes}\)

Two balls are drawn at random, therefore

Total possible outcomes are ¹⁶C₂

n (S) = 120

(i) Let E be the event of getting both white balls

E = {(W) (W)}

n (E) = ⁷C₂ = 21

P (E) = \( \dfrac{ n (E) }{ n (S)}\)

=\( \dfrac{21}{120}\)

= \( \dfrac{7}{40}\)

(ii) Let E be the event of getting one black and one red ball

E = {(B) (R)}

n (E) = ⁵C₁⁴C₁ = 20

P (E) =\( \dfrac{ n (E) }{ n (S)}\)

= \( \dfrac{20}{120}\)

= \( \dfrac{1}{6}\)

(iii) Let E be the event of getting both balls of same colour

E = {(B) (B)} or {(W) (W)} or {(R) (R)}

n (E) = ⁷C₂+⁵C₂+⁴C₂ = 37

P (E) = \( \dfrac{ n (E) }{ n (S)}\)

= \( \dfrac{37}{120}\)