a car wash has three different types of washes: basic, classic, and ultimate. based on records, 45% of…

a car wash has three different types of washes: basic, classic, and ultimate. based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. some customers also vacuum out their cars after the wash. the car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. the probabilities are displayed in the tree - diagram. what is the probability that a randomly selected customer vacuums their car? 0.05 0.09 0.12 0.25

a car wash has three different types of washes: basic, classic, and ultimate. based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. some customers also vacuum out their cars after the wash. the car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. the probabilities are displayed in the tree - diagram. what is the probability that a randomly selected customer vacuums their car? 0.05 0.09 0.12 0.25

Answer

Answer:

0.25

Explanation:

Step1: Calculate probability for basic - vacuum

Multiply probabilities: $0.45\times0.10 = 0.045$

Step2: Calculate probability for classic - vacuum

Multiply probabilities: $0.35\times0.25= 0.0875$

Step3: Calculate probability for ultimate - vacuum

Multiply probabilities: $0.20\times0.60 = 0.12$

Step4: Sum up probabilities

$0.045 + 0.0875+0.12=0.2525\approx0.25$