Question

Please help!

Event A: At least one die shows a 4
Event B: The sum of the dice is greater than 5

What is P(A)?
What is P(B)?
What is P(A and B)?
What is P(A or B)?
What is P(A|B)?

Answer 1

Are you able to make the Solution set of 'Event A' and 'Event B' ?

Answer 2

You mean a table of the sum of the dice?

Answer 3

I might have gotten this wrong but I got

P(A) = 11/36
P(B) = 13/18
P(A and B) = 1/4
P(A or B) = 7/9
P(A|B) = 9/26

Answer 4

The sample space has 36 possible combinations of numbers. These can be set out in column form as follows:
6,6 5,6 4,6 3,6 2,6 1,6
6,5 5,5 4,5 3,5 2,5 1,5
6,4 5,4 4,4 3,4 2,4 1,4
6,3 5,3 4,3 3,3 2,3 1,3
6,2 5,2 4,2 3,2 2,2 1,2
6,1 5,1 4,1 3,1 2,1 1,1

Answer 5

I confirm your results for P(A) and P(B).

Answer 6

P(A and B) is the intersection of A and B:
\[A \cap B=\frac{1}{4}\]

Answer 7

P(A or B) is A union B:
\[P(A \cup B)=P(A)+P(B)-P(A \cap B)=\frac{11}{36}+\frac{13}{18}-\frac{1}{4}=\frac{7}{9}\]

Answer 8

I confirm your result for P(A|B)

Answer 9

@notabakery Do you need any explanation?

Answer 10

Nope, that makes a lot more sense! Thank you!

Answer 11

You're welcome :)