A student observed the color and type of vehicle that passed by his school for an hour. The two-way table is given below:
| | Red | Blue | White | Total |
| :---- | :-- | :--- | :---- | :---- |
| Car | 19 | 6 | 7 | 32 |
| Truck | 8 | 16 | 9 | 33 |
| SUV | 3 | 10 | 22 | 35 |
| Total | 30 | 32 | 38 | 100 |
What is the probability that a randomly selected vehicle from this observation is a car, given that it's blue?
[tex]P(\text { Car } \mid \text { Blue })=[?] %[/tex]
Round your answer to the nearest whole percent.
Answer (2)
Find the number of blue cars: 6.
Find the total number of blue vehicles: 32.
Calculate the conditional probability: P ( Car ∣ Blue ) = 32 6 = 16 3 .
Convert to percentage and round: 16 3 × 100 ≈ 19% .
Explanation
Understand the problem We are given a two-way table that shows the counts of vehicle types (Car, Truck, SUV) and colors (Red, Blue, White). The question asks for the probability that a randomly selected vehicle is a car, given that it is blue. This is a conditional probability problem.
Identify the necessary values from the table To find the conditional probability P ( Car ∣ Blue ) , we use the formula: P ( Car ∣ Blue ) = Total number of blue vehicles Number of blue cars From the table, we can see that the number of blue cars is 6, and the total number of blue vehicles is 32.
Calculate the conditional probability and convert to percentage Now, we can calculate the probability: P ( Car ∣ Blue ) = 32 6 = 16 3 To express this probability as a percentage, we multiply by 100: 16 3 × 100 = 18.75 Rounding this to the nearest whole percent, we get 19%.
State the final answer Therefore, the probability that a randomly selected vehicle is a car, given that it's blue, is approximately 19%.
Examples
Conditional probability is useful in many real-life scenarios. For example, in medical diagnosis, it helps determine the probability of a patient having a disease given a positive test result. In marketing, it can be used to predict the likelihood of a customer making a purchase given they have visited a specific page on a website. In finance, it helps assess the risk of a loan default given certain economic indicators.
The probability that a randomly selected vehicle is a car, given that it's blue, is 19%. This was calculated by dividing the number of blue cars (6) by the total number of blue vehicles (32). After computing the fraction and converting it to a percentage, we rounded to the nearest whole number.
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