a)0.250
b)0.606
In the given question , we observe that
at Elmo's an old-fashioned barber shop in Melbourne, Florida ,66% of all customers get a haircut ,49% get a save and 40% get both.
Probability is simply how likely something is to happen.
Whenever we are unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
The best example for understanding probability is flipping a coin:
There are two possible outcomes—heads or tails.
Independent event:
If two events, A and B are independent then the joint probability is
P(A and B)=P(A∩B)=P(A)P(B)
For example, if two coins are flipped, then the chance of both being heads is 1/2*1/2=1/4
probabilities of different events are:
P(Haircut)=66%=66/100=0.66
P(Shave)=49%=49/100=0.49
P(both)=40%=40/100=0.40
a) we have to find the probability that a randomly selected person doesn't get a shave and doesn't get a haircut.
P(no haircut ∩ no shave)=1-P(haircut ∪ shave)
=1-[P(haircut)+P(shave)-P(both)]
=1-[0.66+0.49-0.40]
=1-0.75
=0.250
b) we have to find the probability that a randomly selected person gets a shave, given that they get a haircut.
P(Shave/Haircut)=P(Both)/P(Haircut)
=0.40/0.66
=0.606
Hence, final answer is
a) the probability that a randomly selected person doesn't get a shave and doesn't get a haircut=0.250
b)the probability that a randomly selected person gets a shave, given that they get a haircut=0.606
learn more about probability here brainly.com/question/11234923
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