Answer to Question #264707 in Statistics and Probability for aaa

Question

An experiment involves tossing a pair of dice, one green and one red, and recording the numbers that come up. Assuming that all elements of the sample space S are equally likely to occur.

Event A is the sum of the two recorded numbers that is greater than 8.

Event B is the occurring of 5 on either die.

find ( A ∩ B )

Answer 1

For event A, the sample space is $A=\{(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\}$

For event B, the sample space is,

$B=\{(1,5),(2,5),(3,5),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,5)\}$

Now, $A\cap B$ consist of all elements in both events A and B.

Therefore,

$A\cap B=\{(4,5),(5,4),(5,5),(5,6),(6,5)\}.$