Dice Probability An unbiased dice is thrown examples

1) An unbiased dice is thrown. What is the probability that the number is Even

Solution:
Total number of outcomes possible when a die is thrown = 6,
i.e.

S={1,2,3,4,5,6} $S = {1,2,3,4,5,6}$

$:.n(S)=6$

Let

$E$ = event of getting a number is even

$:.E = {2,4,6}$

$:.n(E) = 3$

$:.P(E)=(n(E))/(n(S))=3/6=1/2$

2) An unbiased dice is thrown. What is the probability that the number is Multiple/Divide by 3

Solution:
Total number of outcomes possible when a die is thrown = 6,
i.e.

$S = {1,2,3,4,5,6}$

$:.n(S)=6$

Let

$E$ = event of getting a number divide by 3

$:.E = {3,6}$

$:.n(E) = 2$

$:.P(E)=(n(E))/(n(S))=2/6=1/3$

3) An unbiased dice is thrown. What is the probability that the number is <= 4

Solution:
Total number of outcomes possible when a die is thrown = 6,
i.e.

$S = {1,2,3,4,5,6}$

$:.n(S)=6$

Let

$E$ = event of getting a number

$<=$ 4

$:.E = {1,2,3,4}$

$:.n(E) = 4$

$:.P(E)=(n(E))/(n(S))=4/6=2/3$

4) An unbiased dice is thrown. What is the probability that the number is Prime

Solution:
Total number of outcomes possible when a die is thrown = 6,
i.e.

$S = {1,2,3,4,5,6}$

$:.n(S)=6$

Let

$E$ = event of getting a number is prime

$:.E = {2,3,5}$

$:.n(E) = 3$

$:.P(E)=(n(E))/(n(S))=3/6=1/2$

5) An unbiased dice is thrown. What is the probability that the number is >= 5

Solution:
Total number of outcomes possible when a die is thrown = 6,
i.e.

$S = {1,2,3,4,5,6}$

$:.n(S)=6$

Let

$E$ = event of getting a number

$>=$ 5

$:.E = {5,6}$

$:.n(E) = 2$

$:.P(E)=(n(E))/(n(S))=2/6=1/3$

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1. An unbiased dice is thrown examples