Question

leni is paid 50 whenever the results of tossing a two coin are both tail but she pays 20 whenever the result are not both tails. what is his expected gain loss pair toss

Answer 1

The expected gain/loss for a pair toss is -2.5.

Step-by-step explanation:

To find the expected gain or loss for pair toss, we need to calculate the probability of getting both tails and the expected gain/loss for each outcome. Let's denote the probability of getting both tails as p(TT) and the expected gain for this outcome as +50. The probability of not getting both tails is 1 - p(TT) and the expected loss for this outcome is -20. Now we can calculate the expected gain/loss by multiplying the probabilities with their respective gains/losses, and summing them up:

Expected gain/loss = p(TT) * (+50) + (1 - p(TT)) * (-20)

To find p(TT), we need to consider the probability of getting a tail on each coin toss. Assuming the two coins are fair, the probability of getting a tail on each toss is 1/2. Since the coin tosses are independent, the probability of getting both tails is (1/2) * (1/2) = 1/4.

Substituting this value into the formula:

Expected gain/loss = (1/4) * (+50) + (1 - 1/4) * (-20) = 12.5 - 15 = -2.5

Therefore, the expected gain/loss for a pair toss is -2.5.