Respuesta :
Answer: The likelihood of winning the bet is [tex] \frac{1}{16} [/tex].
Number of racers in each run = 8
Since each race stands an equal chance of winning, so
[tex] P(winning) = \frac{No.of favorable outcomes}{Total number of outcomes} [/tex]
Since there can be only one winner, number of favourable outcomes is 1,
[tex] P(winning) = \frac{1}{8} [/tex]
Either racer A or racer B can win the race. These events are mutually exclusive. Hence,
[tex] P(A or B winning) = P(A) + P(B) [/tex]
[tex] P(A or B winning) = \frac{1}{8} + \frac{1}{8} [/tex]
[tex] P(A or B winning) = \frac{2}{8} = \frac{1}{4} [/tex]
At the beginning of the race, the probability each racer finishing second is:
[tex] P(finishing second) = \frac{No.of favorable outcomes}{Total number of outcomes} [/tex]
Only one racer can finish second, so the number of favourable outcomes is 1.
[tex] P(finishing second) = \frac{1}{8} [/tex]
Either racer A or racer B can finish second. Since these events are mutually exclusive,
[tex] P(A or B finishing second) = P(A) + P(B) [/tex]
[tex] P(A or B finishing second) = \frac{2}{8} = \frac{1}{4} [/tex]
We can win the bet only if both the racers we select finish first and second.
[tex] P(winning the bet) = P(A or B winning) * P(A or B finishing second)
[/tex]
[tex] P (winning the bet) = \frac{1}{4} * \frac{1}{4} [/tex]
[tex] P(winning the bet) = \frac{1}{16} [/tex]
