Three coins are tossed hint you may want to draw a tree diag

Three coins are tossed. (hint you may want to draw a tree diagram to list the sample space.)

a)         Determine the number of points in the sample space.

b)         Determine the probability that no heads are tossed.

c)         Determine the probability that exactly one head is tossed.

d)         Determine the probability that three heads are tossed.

Solution

a)

Three coins

Each coin toss can result in 2 outcomes --> H or T

So, total number of outcomes = 2*2*2 = 2^3 = 8 outcomes

So, we have 8 points in the sample space ----> ANSWER

For your reference and for the remaining 3 questions, the sample space has been written below :

HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

b)

P(no heads) :

From the above sample space, we can see there is only one outcome where no heads are tossed, i.e TTT

So, 1 out of 8

P(no heads) = 1/8 --> ANSWER

c)

P(exactly 1 head) :

HTT
THT
TTH

3 out of 8

3/8 --> ANSWER

d)

P(3 heads) ---> HHH

1 out of 8

1/8 ---> ANSWER