Answer:
a) 0.167 b)0.056 c)0.023
Step-by-step explanation:
We are given the following information:
Sample space = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Total number of outcomes = 36
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
a) P(sum is 7)
Sum 7 possible outcomes = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
[tex]= P = \displaystyle\frac{6}{36} = \displaystyle\frac{1}{6} = 0.167[/tex]
b) P(sum is 11)
Sum 11 possible outcomes = {(5,6), (6,5)}
[tex]= P = \displaystyle\frac{2}{36} = \displaystyle\frac{1}{18} = 0.056[/tex]
c) P( sum is 7 or sum is 11)
[tex]= P(\text{sum is 7}) + P(\text{sum is 11}) - (P(\text{sum is 7}\cap \text{sum is 11})) \\= \displaystyle\frac{6}{36} + \displaystyle\frac{2}{36} + 0\\\\= \displaystyle\frac{8}{36} = \displaystyle\frac{2}{9} = 0.223[/tex]
The probability of obtaining the following outcomes from two die rolls are :
From the sample space of the sum of two fair dice attached below ;
Recall :
Probability = (Required outcome ÷ total possible outcomes)
Total possible outcomes = 36
1.) Probability of getting a sum of 7 :
Number of outcomes that sums up to 7 = 6
Therefore ;
P(Sum of 7) = 6/36 = 1/6
2.) Probability of getting a sum of 11 :
Number of outcomes that sums up to 11 = 2
Therefore ;
P(Sum of 11) = 2/36 = 1/18
3.) Probability of getting a sum of 7 or 11 :
Number of outcomes that sums up to 11 or 7 = (6 + 2) = 8
Therefore ;
P(Sum of 11 or 7) = 8/36 = 2/9
The probability of getting a sum of 7, 11 and (11 or 7) are 1/6, 1/18 and 2/9 respectively.
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