Question

if the probability of a winning a race is 1/6 and the probability of a horse b winning the same race is 1/4 -----is the probability that one of the horses will win

( a)5/12


(b)7/12


(c)1/12


(d)1/7​

Answer 1

Solution:-

If the probability of a winning a race is 1/6 then,

P(A) = 1/6

If the probability of a horse b winning the same race is 1/4 then,

P(B) = 1/4

the probability that one of the horses will win = P(A) + P(B)

= 1/6+1/4

= (2+3)/12

= 5/12

Hence , the option (a) is correct.(Ans)

Answer 2

Given:

The probability of a winning a race is 1/6 and the probability of a horse b winning the same race is 1/4

To find:

The probability that one of the horses will win

Solution:

From given, we have,

The probability of a winning a race is 1/6 then,

P(A) = 1/6

⇒ P(A') = 1 - P(A)

⇒ P(A') = 1 - 1/6 = 5/6

If the probability of a horse b winning the same race is 1/4 then,

P(B) = 1/4

⇒ P(B') = 1 - P(B)

⇒ P(B') = 1 - 1/4 = 3/4

The probability that one of the horses will win

= P(A) × P(B') + P(B)  × P(A')

= 1/6 × 3/4 + 1/4  × 5/6

= 3/24 + 5/24

= 8/24

= 1/3

Therefore, the probability that one of the horses will win is 1/3