Question

An experiment consists of tossing a coin three times and record the outcomes.

a. Draw a probability tree illustrating all the possible outcomes of this experiment.

b.What is the probability of at least one tail when tossing three coins?

Answer 1

Solution:

An experiment consists of tossing a coin three times and record the outcomes

Part a) Draw a probability tree illustrating all the possible outcomes of this experiment.

Three coins are tossed at a time.

So following tree diagram is for tossing of three coins.

Thus possible outcomes are:

S : { HHH, HHT , THH , HTT , THH , THT , TTH , TTT }

Thus n = total outcomes in sample space = 8

Part b) What is the probability of at least one tail when tossing three coins?

P( At least one tail ) = .........?

Let E = Event of At least one tail

So from tree diagram , we can see following outcomes represents at least one tail

E = { HHT , THH , HTT , THH , THT , TTH , TTT}

thus m = number of outcomes in event E = 7

Thus

P(E) = m / n

P(E) =7/8

P(E) =0.875

Thus P( At least one tail ) = 0.875