Final answer:
The experiment consists of tossing a penny, nickel, dime, and a quarter. The sample space for the experiment is listed, and the probabilities of obtaining a certain outcome are calculated. The probability of obtaining two heads and two tails is determined, along with the probability of obtaining at least one head.
Step-by-step explanation:
The experiment consists of tossing a penny, a nickel, a dime, and a quarter.
a) The sample space or outcomes for the experiment could be:{HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT} where H = head and T = tail.
b) The probability of obtaining a tail on the penny and dime and a head on the quarter and nickel each is 0.5, since each coin has two sides (head and tail) which are equally likely to come up.
c) The probability of obtaining two heads and two tails is 0.25, since there are 4 possible outcomes (HHHT, HHTH, HTHH, THHH) out of the total 16 outcomes in the sample space.
d) The probability of obtaining at least one head in the experiment can be calculated by finding the probability of obtaining four tails (complementary event) and subtracting it from 1. The probability of obtaining four tails is 0.0625, so the probability of obtaining at least one head is 1 - 0.0625 = 0.9375.