Question

An experiment involves tossing a penny, nickel, dime, and quarter. What are the outcomes of the experiment?

a) List the explicit outcomes.
b) Determine the probability of obtaining a tail on the penny and dime and a head on the quarter and nickel.
c) Calculate the probability of obtaining two heads and two tails.
d) Find the probability of obtaining at least one head in the experiment.

Answer 1

The sample space for the experiment is listed, along with the probabilities of various outcomes.

Step-by-step explanation:

The sample space for a coin toss experiment involving a penny, nickel, dime, and quarter is as follows:

• HHHH
• HHHT
• HHHT
• ...

The probability of obtaining a tail on the penny and dime and a head on the quarter and nickel is calculated by multiplying the probabilities of each individual event together. Since each coin has two possible outcomes, the probability is 1/2 * 1/2 * 1/2 * 1/2 = 1/16.

The probability of obtaining two heads and two tails can be calculated by considering the number of favorable outcomes to the total number of possible outcomes. In this case, there are 6 favorable outcomes and 16 possible outcomes, so the probability is 6/16 = 3/8.

The probability of obtaining at least one head in the experiment can be determined by considering the complementary event of obtaining no heads. There are 3 favorable outcomes (HTTT, THTT, and TTHT) and 16 possible outcomes, so the probability is 3/16.