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 $)=$ $\square$

Question

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 $)=$ $\square$

Accepted Answer

∻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: $P( ext{haircut} \mid ext{permanent}) = \frac{P( ext{haircut and permanent})}{P( ext{permanent})}$. ‖ ‖ step 5 ⋮ Substitute the calculated values into the formula to find the conditional probability. ‖ ∻Answer∻ ⚹ $P( ext{haircut} \mid ext{permanent}) = \frac{45\%}{65\%} = \frac{9}{13}$ ⚹ ∻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.⚹◊What is the formula for calculating conditional probability in this scenario using the information from the Venn diagram?⍭ Generate me a similar question◊

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