Question

Suppose a die is rolled twice and let
B = {first toss is a 3} D = {second toss is a 3}
Find the requested probability. (Enter the probability as a fraction.)
P(B ∪ D)

Answer 1

it would help if you looked at a table of all 36 possibilities

Answer 2

http://www.learner.org/workshops/algebra/workshop5/images/chart2.gif

Answer 3

so there's 6 possibilities for both, so now what do I do?

Answer 4

you want their union

Answer 5

lets identify B and D

first toss three
B= { (3,1 ) (3,2) ( 3,3) (3,4) (3 , 5 ) (3 , 6) }

second toss is a three

D = { (1,3) (2,3) (3,3) (4,3) ( 5,3 ) ( 6,3) }

Answer 6

B union D = { (3,1 ) (3,2) ( 3,3) (3,4) (3 , 5 ) (3 , 6) (1,3) (2,3) (3,3) (4,3) ( 5,3 ) ( 6,3) }

do you see there is an term counted twice, we have to delete that

Answer 7

B union D fixed = { (3,1 ) (3,2) (3,4) (3 , 5 ) (3 , 6) (1,3) (2,3) (3,3) (4,3) ( 5,3 ) ( 6,3) }

Answer 8

the sample point (3,3) was counted twice , since it was in the intersection of the column and row

Answer 9

P(B union D ) = P(B) + P(D) - P( B & D )

Answer 10

so there are two ways to do this, you can manually count up the points in the sample space

Answer 11

or you can use the addition formula

Answer 12

which way do you recommend?

Answer 13

either is fine. the first way gives you

11/36

the second way gives you

1/6 + 1/6 - 1/36

Answer 14

Thank you so much!!