Question

Debra is the coach of a junior ultimate team. Based on the team's record, it has a 70% chance of winning on calm days and a 50% chance of winning on windy days. Tomorrow, there is a 30% chance of high winds. There are no ties in ultimate. What is the probability that Debra's team will win tomorrow? a. 0.35 b. 0.64 c. 0.49 d. 0.15

Answer 1

The probability that Debra's team will win tomorrow is 0.49.

Step-by-step explanation:

To find the probability that Debra's team will win tomorrow, we need to consider the chance of calm days and windy days. Since tomorrow there is a 30% chance of high winds, there is a 70% chance of calm days.

On calm days, the team has a 70% chance of winning and on windy days, they have a 50% chance of winning. Therefore, the probability of winning tomorrow can be calculated as:

Probability of winning = (Probability of calm day) * (Probability of winning on calm day) + (Probability of windy day) * (Probability of winning on windy day)

Probability of winning = 0.7 * 0.7 + 0.3 * 0.5 = 0.49

Therefore, the probability that Debra's team will win tomorrow is 0.49.

Answer 2

The probability that Debra's team will win tomorrow is 0.64 (option b).

Step-by-step explanation:

Calculate the probability of a calm day: 100% - 30% chance of wind = 70% chance of calm.

Use the win probabilities:

Win on a calm day: 70% chance * 70% win probability = 0.49.

Win on a windy day: 30% chance * 50% win probability = 0.15.

Combine probabilities: Since the two scenarios are mutually exclusive (calm or windy), add the probabilities to get the overall win probability: 0.49 + 0.15 = 0.64.

Therefore, Debra's team has a 64% chance of winning tomorrow's game.