Question

35. What is the probability of rolling a sum of 8 on at least one of two rolls of a pair of number cubes?

Answer 1

its the number of ways of getting 8 out of all the numbers on 2 dice. There are 36 numbers on two dice and 6 ways of getting an 8 so the probability is

6/36 + 6/36 because we are thowing the pair twice

this gives 12/36 = 1/3

Answer 2

there are 5 ways to get an 8

Answer 3

six if 4 and 4 are not chosen as a repeat.

Answer 4

there is only one way to get a 4 and 4...that is you get a 4 then a 4

Answer 5

Ok well the rest is still good just 5/36 instead

Answer 6

it is not...you are missing a little bit

Answer 7

P( A or B)=P(A)+P(B)-P(A and B)

or use the complement

P(A or B)=1-P(A' and B')

Answer 8

but hold on just looked it up cos I was confused and your formula is for events that are not mutually exclusive like pulling a jack and a spade from a deck. These events are exclusive so P(A)+P(B) is the correct probability in this case.

Answer 9

they are not mutually exclusive...they are independent

Answer 10

the formulas I gave always hold true.

you can combine them with independence to get

P(A or B)=P(A)+P(B)-P(A and B)=P(A)+P(B)-P(A)P(B)

or

P(A or B)=1-P(A' and B')=1-P(A')P(B')

Answer 11

\[P(A)+P(B)-P(A)P(B)=\frac{5}{36}+\frac{5}{36}-\frac{5}{36}\frac{5}{36}=\frac{335}{1296}\]

or

\[1-P(A')P(B')=1-\frac{31}{36}\frac{31}{36}=\frac{335}{1296}\]

Answer 12

this also follows a binomial distribution

\[\sum_{x=1}^{2}{2\choose x}\left(\frac{5}{36}\right)^x\left(1-\frac{5}{36}\right)^{2-x}=\frac{335}{1296}\]