Question

if the toss of a coin comes down heads, you win a dollar. if it comes down tails, you lose fifty cents. how much would you expect to gain after 20 tosses? multiple choice $10.00 $7.50 $15.00

Answer 1

After 20 fair coin tosses where heads wins you $1 and tails loses you $0.50, you would expect to gain $5.00.

Step-by-step explanation:

The question involves calculating the expected gain from tossing a coin with different outcomes for heads and tails over a series of trials. With a fair coin, since the probability of getting heads (winning $1) or tails (losing $0.50) is equal, we can calculate the expected value per toss and then multiply by the number of tosses to find the overall expected gain.

Step-by-Step Calculation

1. Calculate the expected value (EV) per toss: EV = (1/2 × $1) + (1/2 × -$0.50).
2. Simplify the calculation: EV = $0.50 - $0.25 = $0.25.
3. Multiply the EV per toss by the number of tosses (20): $0.25 × 20 = $5.00.

Therefore, after 20 tosses, you would expect to gain $5.00.