Please show all your work! Thanks! 4. Three fair dice are rolled and the number
ID: 3357798 • Letter: P
Question
Please show all your work! Thanks!
4. Three fair dice are rolled and the number of dots showing on each die is recorded. (a) Without actually listing them, how many equally likely outcomes are in the (b) Find the probability that the total number of dots showing on the three dice is (c) Find the probability that the total number of dots showing on the three dice is (d) Find the probability that the total number of dots showing on the three dice is Some of the outcomes would include (1,2,5), (6,2,3) and (4,4,4). sample space? three. eighteen. four.Explanation / Answer
a) There are 6 outcomes for each of the three dice. Therefore the total number of equally likely outcomes on three dice throws would be computed as: 6*6*6 = 216 outcomes.
b) The probability of getting a total of three on the 3 dice throws is computed as:
= Probability of getting the one dot face on each of the 3 dice
= 1/216
= 0.0046
Therefore 0.0046 is the required probability here.
c) The probability of getting a total of eighteen on the 3 dice throws is computed as:
= Probability of getting the six dot face on each of the 3 dice
= 1/216
= 0.0046
Therefore 0.0046 is the required probability here.
d) Now we can have four in the following combinations:
(1, 1, 2 ) , (1, 2, 1) , (2, 1, 1 )
Therefore there are 3 combinations here
Therefore the required probability here would be: = 3/216 = 0.0139
Therefore 0.0139 is the required probability here.
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