a die is rolled repeatedly and the total number of times (frequency) each face o

Question

a die is rolled repeatedly and the total number of times (frequency) each face occurs is recorded. The resules are as follows:

a) complete the table to find a probability distribution for each side of the die to turn up on a single roll.

b) what is the probability that a die comes up even?

c) find the probability that the die shows a number greater than 4.

d) find the probability that the die does not come up 1.

e) the odds the probability does not come up 1.

face value 1 2 3 4 5 6 frequency 237 168 180 103 165 147 probability

Explanation / Answer

a)

Here, there are 1000 rolls. Thus, to get the probabilities, we divide the frequencies by 1000:

b)

P(even) =P(2) + P(4) + P(6) = 0.168 + 0.103 + 0.147 = 0.418 [ANSWER]

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c)

P(greater than 4) = P(5) + P(6) = 0.165 + 0.147 = 0.312 [ANSWER]

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D)

P(not 1) = 1 - P(1) = 1 - 0.237 = 0.763 [ANSWER]

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e)

odds = P(not 1) / P(1) = 0.763/0.237 = 3.219409283 [ANSWER]

face value frequency probability 1 237 0.237 2 168 0.168 3 180 0.18 4 103 0.103 5 165 0.165 6 147 0.147

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