To verify whether the given odds are consistent, we can perform a simple calculation. The odds for an event can be expressed as a ratio of the number of favorable outcomes to the number of unfavorable outcomes.
Let's start by calculating the odds of winning. According to the coach, the odds of winning are 3:1. This means that for every 3 favorable outcomes (winning), there is 1 unfavorable outcome (not winning). Therefore, the probability of winning can be calculated as:
Probability of winning = Favorable outcomes / (Favorable outcomes + Unfavorable outcomes)
= 3 / (3 + 1)
= 3/4
= 0.75 (or 75%)
Now let's calculate the odds against losing. The odds against losing are given as 5:1. This implies that for every 5 unfavorable outcomes (losing), there is 1 favorable outcome (not losing, which includes winning or tying). Therefore, the probability of not losing can be calculated as:
Probability of not losing = Favorable outcomes / (Favorable outcomes + Unfavorable outcomes)
= 1 / (5 + 1)
= 1/6
≈ 0.167 (or 16.7%)
Finally, let's calculate the odds against a tie. The odds against a tie are given as 7:1. This means that for every 7 unfavorable outcomes (a tie), there is 1 favorable outcome (not tying, which includes winning or losing). Therefore, the probability of not tying can be calculated as:
Probability of not tying = Favorable outcomes / (Favorable outcomes + Unfavorable outcomes)
= 1 / (7 + 1)
= 1/8
= 0.125 (or 12.5%)
Now, if we add up the probabilities of winning (0.75), not losing (0.167), and not tying (0.125), the total probability should equal to 1 (or 100%). Let's check if this holds true:
0.75 + 0.167 + 0.125 = 1.042
As we can see, the sum is greater than 1, which means the given odds cannot be accurate. In a valid scenario, the sum of probabilities should always equal 1.
Therefore, the coach's claim about the odds is not correct because the probabilities derived from the odds do not add up to 1.