Question

Math

Posted 3 months ago

```
A salon owner noted what types of services its clients requested last week. Here are the results:
Find the probability that a randomly chosen client requested a haircut given they requested a permanent.
$P($ haircut $\mid$ permanent $)=$ $\square$
```

Sign in to unlock the answer

Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Identify the relevant sections of the Venn diagram for the conditional probability

step 2

Calculate the total percentage of clients who requested a permanent service. This includes those who requested Permanent only, Haircut and Permanent, Dye and Permanent, and all three services

step 3

Calculate the percentage of clients who requested both a haircut and a permanent service. This includes those who requested Haircut and Permanent, and all three services

step 4

Use the formula for conditional probability: $P(\text{haircut} \mid \text{permanent}) = \frac{P(\text{haircut and permanent})}{P(\text{permanent})}$

step 5

Substitute the calculated values into the formula to find the conditional probability

Answer

$P(\text{haircut} \mid \text{permanent}) = \frac{45\%}{65\%} = \frac{9}{13}$

Key Concept

Conditional Probability

Explanation

The conditional probability of an event A given event B is the probability that event A occurs given that event B has already occurred. It is calculated by dividing the probability of both events A and B occurring by the probability of event B.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question