Question

Construct a sample space (list or make a tree diagram of all of the outcomes) for the experiment of

a) rolling a 12 sided die and flipping a coin at the same time. Assuming each outcome is equally likely, what is the probability of: DO NOT REDUCE

b) rolling a number less than 4 and getting heads?

c) rolling an odd number and getting tails?

d) rolling a 7 and getting ( heads or tails)

Answer 1

a) Sample Space:

Possible outcomes of the die	Possible outcomes on flipping a coin
H	T
1	1,H	1,T
2	2,H	2,T
3	3,H	3,T
4	4,H	4,T
5	5,H	5,T
6	6,H	6,T
7	7,H	7,T
8	8,H	8,T
9	9,H	9,T
10	10,H	10,T
11	11,H	11,T
12	12,H	12,T

Total number of cases is 24.

b)

Number of cases of the event of rolling a number less than 4 and getting heads is 3.

Hence, required probability is 3/24 = 1/8.

c)

Number of cases of the event of rolling an odd number and getting tails is 6

Hence, required probability is 6/24 = 1/4.

d)

Number of cases of the event of rolling a 7 and getting ( heads or tails) is 2

Hence, required probability is 2/24 = 1/12.