a student observed the color and type of vehicle that passed by his school for an hour. the two - way table…

a student observed the color and type of vehicle that passed by his school for an hour. the two - way table is given below:\n| | red | blue | white | total |\n|--|--|--|--|--|\n| car | 19 | 6 | 7 | 32 |\n| truck | 8 | 16 | 9 | 33 |\n| suv | 3 | 10 | 22 | 35 |\n| total | 30 | 32 | 38 | 100 |\nwhat is the probability that a randomly selected vehicle from this observation is a car, given that its blue?\np(car | blue) = ?%\nround your answer to the nearest whole percent.

a student observed the color and type of vehicle that passed by his school for an hour. the two - way table is given below:\n| | red | blue | white | total |\n|--|--|--|--|--|\n| car | 19 | 6 | 7 | 32 |\n| truck | 8 | 16 | 9 | 33 |\n| suv | 3 | 10 | 22 | 35 |\n| total | 30 | 32 | 38 | 100 |\nwhat is the probability that a randomly selected vehicle from this observation is a car, given that its blue?\np(car | blue) = ?%\nround your answer to the nearest whole percent.

Answer

Explanation:

Step1: Recall conditional - probability formula

$P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of the table, $P(\text{Car}|\text{Blue})=\frac{\text{Number of blue cars}}{\text{Total number of blue vehicles}}$.

Step2: Identify values from the table

The number of blue cars is 6, and the total number of blue vehicles is 32.

Step3: Calculate the probability

$P(\text{Car}|\text{Blue})=\frac{6}{32}=\frac{3}{16}= 0.1875$.

Step4: Convert to percentage

$0.1875\times100 = 18.75%$.

Step5: Round to the nearest whole - percent

Rounding 18.75% gives 19%.

Answer:

19%