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Chapter 2: Problem 89

A box contains 7 red, 5 white, and 4 black balls. What is the probability of your drawing at random one red ball? One black ball?

Short Answer

Expert verified
The probability of drawing a red ball is \( \frac{7}{16} \), and the probability of drawing a black ball is \( \frac{1}{4} \).

Step by step solution

01

Identify the total number of balls in the box

To calculate the probability, we first need to know the total number of balls in the box. We can find this by adding the number of red, white, and black balls. Total number of balls = 7 red + 5 white + 4 black = 16 balls
02

Calculate the probability of drawing a red ball

Now that we know the total number of balls in the box, we can find the probability of drawing a red ball. According to the problem, there are 7 red balls in the box. Using the formula for probability, we can find the probability of drawing a red ball. Probability of drawing a red ball = (number of red balls) / (total number of balls) = \( \frac{7}{16} \)
03

Calculate the probability of drawing a black ball

Similarly, we can find the probability of drawing a black ball. According to the problem, there are 4 black balls in the box. Using the formula for probability, we can find the probability of drawing a black ball. Probability of drawing a black ball = (number of black balls) / (total number of balls) = \( \frac{4}{16} \)
04

Simplify the probabilities

Lastly, we can simplify both probabilities by reducing them to their lowest terms. Probability of drawing a red ball = \( \frac{7}{16} \) (already in lowest terms) Probability of drawing a black ball = \( \frac{4}{16} \) = \( \frac{1}{4} \) Thus, the probability of drawing a red ball is \( \frac{7}{16} \), and the probability of drawing a black ball is \( \frac{1}{4} \).

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