Refer to Exercise probabilities. Find the following probabilities. a. Two heads
b. One head
c. At least one head
d. At least two heads

Required:
Draw a probability tree to describe the flipping of three fair coins.

Step-by-step explanation:

Probability is defined as the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

probability = n{E}/n{S}

n(E) is the total number of events

n{S} is the total number of sample space.

For a coin that is tossed 3times, the possible outcome are:

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

The total number of sample space is n(S) = 2³ = 8

n{S} = 8

a) probability of getting two heads.

Events E = {HHH, HHT, HTH, THH}

n(E) = 4

Pr(getting two heads) = 4/8 = 1/2

b) probability of getting one head.

Events E = {HTT, THT, TTH}

n(E) = 3

Pr(getting one head) = 3/8

c) probability of getting at least one head means probability of getting 1 head and more but not less than a head.

Events E = {HHH, HHT, HTH, HTT, THH, THT, TTH}

n(E) = 7

Pr(getting at least one head) = 7/8

d) probability of getting at least two heads means probability of getting 2 head and more but not less than 2 head.

Events E = {HHH, HHT, HTH, THH}

n(E) = 4

Pr(getting at least two head) = 4/8 = 1/2

Find the tree diagram in the attachment below.

the answer is d. 75%