Question

Suppose we toss a two-sided coin (H on one side and T on the other side )n=3701 times. In any given toss, the probability the coin comes up H is p=P(H)=0.73. Each time the coin comes up H we give Tom 2 dollars and each time the coin comes up T we take from Tom 1 dollar (so Tom either gets 2 or gets - 1, i.e., loses 1 dollar). How many dollars do we expect Tom will get per toss?

Answer 1

Tom will expect to get $1.19 per toss of the biased coin. This is calculated using the expected value formula, considering the given probabilities and monetary outcomes for heads and tails.

Step-by-step explanation:

To determine how many dollars Tom will expect to get per toss of a biased coin, you calculate the expected value. The probability of getting a head (H) is given as P(H) = 0.73, and the probability of getting a tail (T) is P(T) = 1 - P(H) = 0.27, since there are only two possible outcomes and their probabilities must add up to 1.

The expected value per toss (E) can be calculated by multiplying the outcome of each event by its probability and then adding these products together: E = (value for H × P(H)) + (value for T × P(T)). Substituting the given values, we have E = ($2 × 0.73) + (-$1 × 0.27).

Performing the calculations, E = $1.46 - $0.27 = $1.19. Therefore, the expected amount Tom will get per toss is $1.19.