Question

Two horses are considered for race. The probability of selection of first horse is `1/5  "and that of second is"  2/3`. Find the probability that:

1. both will be selected.
2. only one of them will be selected.
3. none of them will be selected.
4. at least one of them will be selected.

Answer 1

Let, the probability of select of first horse, P(A) = `1/5`

and that of second horse, P(B) = `2/3`

`P(barA) or P("not" A)`

= `1−1/5`

= `4/5`

`P(barB) = 1 − 2/3`

= `1/3`

(i) Both will be selected:

P(A ∩ B) = P(A) x P(B)

= `1/5 × 2/3`

= `2/15`

(ii) only one of them:

= `P(A) P(barB) + P(B) P(barA)`

= `1/5 × 1/3 + 2/3 × 4/5`

= `9/15`

(iii) none of them:

= `P(barA) × P(barB)`

= `4/5 × 1/3`

= `4/15`

(iv) at least one of them:

`P(A) P(barB) + P(barA) P(B) + P(A) × P(B)`

= `1/5 × 1/3 + 2/3 × 4/5 + 1/5 × 2/3`

= `9/15 + 2/15`

= `11/15`