Answer:
P(rolling the die results in a 3 or a 6)=0.3333
P(rolling the die results in not getting a 6)=0.8333
P(rolling the die results in the number being either greater than 2 or less than 5)=0.3333
P(rolling the die results in an even number or a 5)=0.6667
P( rolling the die twice results in a 6 followed by a 4)=0.0278
P(rolling the die three times results in all 6's)=0.0046
Step-by-step explanation:
a)
As the all outcomes are equally likely, so each number has equal probability of occurring.
For six sided die the sample space is {1,2,3,4,5,6} and each outcome has equal probability of 1/6.
1)
P(rolling the die results in a 3 or a 6)
P(rolling the die results in a 3 or a 6)=P(3)+P(6)=1/6+1/6=2/6=1/3
P(rolling the die results in a 3 or a 6)=0.3333
P(rolling the die results in not getting a 6)
P(rolling the die results in not getting a 6)=1-P(6)=1-1/6=5/6
P(rolling the die results in not getting a 6)=0.8333
P(rolling the die results in the number being either greater than 2 or less than 5)
number either greater than 2 or less than 5={3,4}
P(rolling the die results in the number being either greater than 2 or less than 5)=2/6=1/3
P(rolling the die results in the number being either greater than 2 or less than 5)=0.3333
P(rolling the die results in an even number or a 5)
number is an even number or a 5={2,4,5,6}
P(rolling the die results in an even number or a 5)=4/6=2/3
P(rolling the die results in an even number or a 5)=0.6667
P( rolling the die twice results in a 6 followed by a 4)
For six sided die rolled twice the sample space is
S={(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)}.
n(S)=6²=36.
rolling the die twice results in a 6 followed by a 4={(6,4)}
P( rolling the die twice results in a 6 followed by a 4)=1/36.
P( rolling the die twice results in a 6 followed by a 4)=0.0278
P(rolling the die three times results in all 6's)
When three die are rolled the number of outcomes=n(S)=6³=216.
rolling the die three times results in all 6's={(6,6,6)}
P(rolling the die three times results in all 6's)=1/216
P(rolling the die three times results in all 6's)=0.0046
Note: All answers are rounded to four decimal places.
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