Final answer:
The probability that Marshall wins a prize on his second spin of a prize wheel with 4 segments is 0.1875, using the geometric distribution formula. The correct answer is option a. 0.1875.
Step-by-step explanation:
The question asks about the probability that Marshall wins a prize on his second spin of a prize wheel with 4 equally-sized segments, one of which is labeled "winner." This is a problem in the subject of probability and can be solved using the geometric distribution formula:
P(X = k) = (1 - p)k-1p
Where p is the probability of winning on a single spin and k is the number of spins until a win occurs. In this case, p = 1/4 (since one out of four segments is a winner), and k = 2 (because we want to find the probability that he wins on the second spin). Plugging the values into the formula:
P(X = 2) = (1 - 1/4)2-1(1/4)
Calculating the probability:
P(X = 2) = (3/4)1(1/4) = 3/16
When converted to decimal form and rounded to four decimal places, the probability is:
P(X = 2) = 0.1875
Therefore, the correct option is a. 0.1875.