Question

Two dice are rolled.
a. Make a table showing all of the possible outcomes.

b. How many outcomes give a sum of 7?
c. How many outcomes give a sum of 7 or a sum of 11?

d. How many outcomes have either the first die as a 3 or have an even sum

A six-person committee composed of Alice, Ben, Connie, Dolph, Egbert, and Francisco is to select a chairperson, secretary, and treasurer. Nobody can hold more than one of these positions.

e. How many selections are there in which Dolph is either a chairperson or he is not an officer?

f. How many selections are there in which Ben is either chairperson or treasurer?

g. How many selections are there in which either Ben is chairperson or Alice is secretary?

Answer 1

1) Two dice are rolled.

a. The possible outcomes are :

{ (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) }

b. Here we need to find, number of outcomes of sum of 7.

From sample space we get :

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

Hence possible number of outcomes having sum 7 = 6.

c. Here we need to find, number of outcomes having sum 7 or sum 11.

i.e. we need to find,

n( sum 7 ) + n( sum 11)

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

6 + 2 = 8

Hence possible number of outcomes having sum 7 or sum 11 is 8.

d.

Here we need to find, possible number of outcomes either the first die as a 3 or have an even sum :

i.e. we need to find,

n ( first die as 3 ) + n ( an even sum )

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

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

= 6 + 18

= 24