Question

4. A coin is tossed twice.
(a) List the outcomes of the sample space.
(b) List the outcomes of the event of getting at least one tail.
(c) List the outcomes of getting exactly one head.
(d) Write probabilities of the event described in parts (a), (b) and (c) above.
​

Answer 1

Given:

A coin is tossed twice.

To find:

(a) List the outcomes of the sample space.

(b) List the outcomes of the event of getting at least one tail.

(c) List the outcomes of getting exactly one head.

(d) Write probabilities of the event described in parts (a), (b) and (c) above.

Solution:

Combinations are: {(H,H) , (H,T) , (T,H) , (T,T)}

a) List the outcomes of the sample space.

Outcomes of the sample space are: {(H,H) , (H,T) , (T,H) , (T,T)}

b) List the outcomes of the event of getting at least one tail.

Outcomes of the event of getting at least one tail are: {(H,T) , (T,H) , (T,T)}

c) List the outcomes of getting exactly one head.

Outcomes of getting exactly one head are: {(H,T) , (T,H)}

d) Write probabilities of the event described in parts (a), (b) and (c) above.

P = Total no. of required events / Total no. of events

P(a) = 4 / 4 = 1

P(b) = 3 / 4

P(c) = 2 / 4 = 1 / 2