three students A,Band c are in a swiming race ,AandB have the same probability of winning and each is twice as likely to win as C

Question

a- what is the probability that A does not win ?

b- what is the probability that Bor C wins ?

Answer 1

Let probability of A winning the race = PA

Let probability of B winning the race = PB

Let probability of C winning the race = PC

 

Given:

PA = PB

PA = 2PC

PB = 2PC

 

We know that probability that either A, B, or C wins is 1

PA+PB+PC = 1

 

Substitute PA = 2PC and PB = 2PC in above equation

2PC + 2PC + PC = 1

5PC = 1 ...divide both sides by 5

PC = 0.2

 

PA = 2PC = 2x0.2 = 0.4

PB = 2PC = 2x0.2 = 0.4

 

a. Probability that A does not win

= 1 - probability that A wins

= 1 - PA = 1 - 0.4

= 0.6 (60% probability that A does not win)

 

b. Probability that B or C wins

= Probability that B wins + Probability that C wins

= PB + PC

= 0.4 + 0.2

= 0.6 (60% probability that B or C wins). This is same as the probability that A does not win.