Question

1. Suppose your peer says, “The referee did not see which team kicked the ball out, so he just guessed. However, there must be a 50% chance he is correct because there are only 2 possible outcomes: the red team or the white team.”

   1. Explain to your peer why his/her logic is flawed.

   2. How might one go about determining the probability that he is correct? Justify your reasoning.

2. Suppose your peer says, “I’m going to flip 2 coins at the same time, and the only 3 possible outcomes are 2 heads, 2 tails, or 1 of each. Thus, the probability that I get 2 heads will be one third.”

   1. Explain to your peer why his/her logic is flawed.

   2. What would the correct classical probability be? Justify your reasoning.

Answer 1

(a)

Peer's logic is flawed because of the following:

It is correct that there are only 2 possible outcomes: the red team or the white team.

So, if p = Probability of Red team kicked the ball, then, Probability of White team kicked the ball = 1 - p.

But, p need not be equal to 0.5.

So, the saying that there must be 50 % chance he is correct is flawed, because it depends on the value of p.

(b)

Thereare4 possible outcomes of flip2coins:
(H, H), (T, T), (H, T), (T, H)

Thus:

The correct classical probability would be as follows:

P(2 Heads) = 1/4 = 0.25

P(2 Tails) = 1/4 =0.25

P(1 of each) = 2/4 = 0.50