A section of an exam contains four True-False questions. A completed exam paper is selected at random, and the four answers are recorded.
a. List all 16 outcomes in the sample space.
b. Assuming the outcomes to be equally likely, find the probability that all the answers are the same.
c. Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is “True.”
d. Assuming the outcomes to be equally likely, find the probability that at most one of the four answers is “True.”
(a) The outcomes are the 16 different strings of 4 true-false answers. These are {TTTT, TTTF, TTFT, TTFF, TFTT, TFTF, TFFT, TFFF, FTTT, FTTF, FTFT, FTFF, FFTT, FFTF, FFFT, FFFF}.
(b) There are 16 equally likely outcomes. The answers are all the same in two of them, TTTT and FFFF. Therefore the probability is 2?16 or 1?8.
(c) There are 16 equally likely outcomes. There are four of them, TFFF, FTFF, FFTF, and FFFT, for which exactly one answer is “True.” Therefore the probability is 4?16 or 1?4.
(d) There are 16 equally likely outcomes. There are five of them, TFFF, FTFF, FFTF, FFFT, and FFFF, for which at most one answer is “True.” Therefore the probability is 5?16.
You might also like to view...
Most modern crop varieties are patented to protect the intellectual property of those who developed them
Indicate whether the statement is true or false
You can use the ____ utility to compare the contents of two files, and if there is a difference, the command reports the location at which the files first start to differ.
A. cmp B. compare C. diff D. difference
A digital-to-analog (D/
A) converter changes data like temperature variations into digital quantities. Indicate whether the statement is true or false
ASE-Style Multiple Choice Which of the following is LEAST-Likely a characteristic of an air transformer?
A. Separates solid particles, such as oil, water, and dirt, out of the compressed air. B. May provide multiple air outlets for spray guns, blow guns, air-operated tools, and so on. C. Filters and regulates the air. D. Removes oil, dirt, and water from the compressed air.