Question

1. answer the questions for game a:

a. what is the probability of player 1 winning?
b. what is the probability of player 2 winning?
c. what is the probability of playing again?
d. is this game fair? explain your answer.

Explanation:

Part a

Step1: Identify total outcomes

When flipping two coins (Coin 1 and the other coin implied in the table), the total number of possible outcomes (considering "Play Again" as a valid outcome for counting) is 4: Heads/Heads, Heads/Tails, Tails/Heads, Tails/Tails.

Step2: Count Player 1 winning outcomes

Player 1 wins only in the Heads/Heads outcome, so there is 1 favorable outcome.

Step3: Calculate probability

Probability is the number of favorable outcomes divided by total outcomes. So, \( \frac{1}{4} \).

Part b

Step1: Identify total outcomes

Total outcomes are still 4 (as in part a).

Step2: Count Player 2 winning outcomes

Player 2 wins in Heads/Tails and Tails/Heads, so there are 2 favorable outcomes.

Step3: Calculate probability

Probability = \( \frac{2}{4}=\frac{1}{2} \).

Part c

Step1: Identify total outcomes

Total outcomes are 4.

Step2: Count "Play Again" outcomes

"Play Again" occurs in Tails/Tails, so there is 1 favorable outcome.

Step3: Calculate probability

Probability = \( \frac{1}{4} \).

Part d

Answer:

s:
a. \( \frac{1}{4} \)
b. \( \frac{1}{2} \)
c. \( \frac{1}{4} \)
d. No, the game is not fair. Player 1 has a \( \frac{1}{4} \) chance to win, and Player 2 has a \( \frac{1}{2} \) chance to win, so their winning probabilities are not equal.