Psychologists sometimes use regular tetrahedral (four-sided) dice (i.e. dice sha
ID: 3172865 • Letter: P
Question
Psychologists sometimes use regular tetrahedral (four-sided) dice (i.e. dice shaped like three-sided pyramids with triangular faces) in their studies of perception. Assume that you have been given a pair of such dice (one die red, one green, say), each face of which is marked 1, 2, 3 or 4. Write down the sample space, St, created by rolling the two dice together and recording all the possible combinations of pairs of values (one provided by the red die. one by the green) that can occur. What is the probability with which each pair of numbers (1r, 1g), (1r, 2g)... (3r, 4g). (4r, 4g) occurs? What are the probabilities with which the sum of each pair of numbers, 2, 3, ... 7, 8, occurs? t(Remember that the components of a sample space are written separately within braces and separated by commas thus: S = {component 1, component 2, etc.}.)Explanation / Answer
Sample space(Red,Green)=(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4).
Probability that a pair occurs= 1/16 i.e prabability of 1 pair amongst the above 16 pairs occuring.
Probability that a sum of 2 occurs= 1 (since only 1 pair (1,1) gives a sum of 2)
Probability that a sum of 3 occurs = 1/2 (Since 2 pairs (1,2) and (2,1) give a sum of 3)
Probability that a sum of 4 occurs= 1/3 {(1,3), (2,2), (3,1)}
Probability that a sum of 5 occurs= 1/4 { (1,4) ,(2,3), (3,2) ,(4,1)}
Probability that a sum of 6 occurs= 1/3 { (2,4), (3,3), (4,2,)}
Probability that a sum of 7 occurs= 1/2 {(3,4), (4,3)}
Probability that a sum of 8 occurs= 1 (4,4)
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