Final answer:
The experiment involves tossing four fair coins and counting the number of tails observed. We can identify the sample points and values of x, calculate p(x) for x=1 and x=2, construct a probability histogram, and calculate P(x=3 or x=4).
Step-by-step explanation:
The experiment involves tossing four fair coins and counting the number of tails observed, denoted as x. Let's go through the questions one by one:
a. The sample points are the possible outcomes of flipping the four coins. The sample points are: TTTT, TTTH, TTHH, THHH, HHHH, TTH, THT, HTT, HHT, THH, HHH, HH, TT, TH, HT, and HH. The corresponding values of x for each sample point are: x=4, x=3, x=3, x=3, x=4, x=3, x=3, x=3, x=2, x=2, x=3, x=2, x=2, x=2, x=1, x=2, and x=2.
The possible values of x are: 4, 3, 2, and 1.
b. To calculate p(x), we divide the number of sample points where x takes on a specific value by the total number of sample points. For x=1, p(x=1) = 2/16 = 1/8. For x=2, p(x=2) = 6/16 = 3/8.
c. To construct a probability histogram for p(x), we plot the possible values of x on the x-axis and the corresponding probabilities on the y-axis. Each value of x will have a bar whose height represents its probability. Since the possible values of x are 4, 3, 2, and 1, we will have bars for each of these values.
d. To calculate P(x=3 or x=4), we sum the probabilities of the sample points where x equals 3 or 4. From part a, we can see that there are 4 sample points where x=4 and 4 sample points where x=3. Therefore, P(x=3 or x=4) = 4/16 + 4/16 = 1/2.