Question

An experiment involves tossing a pair of dice, one green and one red, and recording the numbers that come up.

(a) list the elements corresponding to the event A that the sum is greater than 7;
(b) list the elements corresponding to the event B that a number greater than 5 comes up on the green die;
(c) list the elements corresponding to the event A ∩ B

Answer 1

A ≡ { ( 2, 6 ), ( 3, 5 ), ( 3, 6 ), ( 4, 4 ), ( 4, 5 ), ( 4, 6 ), ( 5, 3 ), ( 5, 4 ), ( 5, 5 ), ( 5, 6 ), ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }

B ≡ { ( 6, 1 ), ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }

A ∩ B ≡ { ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }

Explanation:

Tossing a pair of dice, one green and one red we will have 36 number of outcomes that is below

Let the first outcome be of green and second outcome be of red.

{ ( 1, 1 ), ( 1, 2 ), ( 1, 3 ), ( 1, 4 ), ( 1, 5 ), ( 1, 6 )

( 2, 1 ), ( 2, 2 ), ( 2, 3 ), ( 2, 4 ), ( 2, 5 ), ( 2, 6 )

( 3, 1 ), ( 3, 2 ), ( 3, 3 ), ( 3, 4 ), ( 3, 5 ), ( 3, 6 )

( 4, 1 ), ( 4, 2 ), ( 4, 3 ), ( 4, 4 ), ( 4, 5 ), ( 4, 6 )

( 5, 1 ), ( 5, 2 ), ( 5, 3 ), ( 5, 4 ), ( 5, 5 ), ( 5, 6 )

( 6, 1 ), ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }

Now,

a ) List the elements corresponding to the event A that the sum is greater than 7.

A ≡ { ( 2, 6 ), ( 3, 5 ), ( 3, 6 ), ( 4, 4 ), ( 4, 5 ), ( 4, 6 ), ( 5, 3 ), ( 5, 4 ), ( 5, 5 ), ( 5, 6 ), ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }

b ) List the elements corresponding to the event B that a number greater than 5 comes up on the green die.

B ≡ { ( 6, 1 ), ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }

c ) List the elements corresponding to the event A ∩ B.

A ∩ B ≡ { ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }