Question

question 11 points 2

a survey was conducted in the class about their favorite subjects. 35% of the class voted for math and science. 45% of the class voted for math. find the percent of the class who voted for math also voted for science.

80%
78%

Explanation:

Define the events and given probabilities

Let \(M\) be the event that a student voted for Math, and \(S\) be the event that a student voted for Science.
From the problem description, we are given:

• The percentage of the class who voted for both Math and Science:

$$P(M \cap S) = 35\% = 0.35$$

• The percentage of the class who voted for Math:

$$P(M) = 45\% = 0.45$$

Identify the target probability

We need to find the percent of the class who voted for Math who also voted for Science.
This is a conditional probability problem. We want to find the probability that a student voted for Science, given that they voted for Math:

$$P(S \mid M)$$

Apply the conditional probability formula

Using the formula for conditional probability:

$$P(S \mid M) = \frac{P(M \cap S)}{P(M)}$$

Substitute the given values into the formula:

$$P(S \mid M) = \frac{0.35}{0.45}$$

Calculate the final percentage

Simplify the fraction:

$$P(S \mid M) = \frac{35}{45} = \frac{7}{9} \approx 0.7778$$

Convert this decimal to a percentage:

$$0.7778 \times 100\% \approx 77.8\%$$

Rounding to the nearest whole percent gives \(78\%\).

Answer:

• (A) 80%
• (B) 78% (Correct answer)