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Chapter 23: Problem 529

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 \( \frac{7}{16} \approx 0.4375 \) and the probability of drawing a black ball is \( \frac{1}{4} \) or 0.25.

Step by step solution

01

Find the total number of balls in the box

There are 7 red balls, 5 white balls, and 4 black balls in the box. We will add them all to find the total number of balls: Total number of balls = 7 (red) + 5 (white) + 4 (black) = 16 balls
02

Calculate the probability of drawing a red ball

To find the probability of drawing a red ball, we will use the probability formula with the number of red balls (7) as our favorable outcome and the total number of balls (16) as the possible outcomes: Probability of red ball = (Number of red balls) / (Total number of balls) Probability of red ball = 7 / 16 Therefore, the probability of drawing a red ball is 7/16 or approximately 0.4375.
03

Calculate the probability of drawing a black ball

Similarly, to find the probability of drawing a black ball, we will use the probability formula with the number of black balls (4) as our favorable outcome and the total number of balls (16) as the possible outcomes: Probability of black ball = (Number of black balls) / (Total number of balls) Probability of black ball = 4 / 16 Therefore, the probability of drawing a black ball is 4/16 or 1/4 or 0.25. In conclusion, the probability of drawing a red ball is 7/16 or approximately 0.4375, and the probability of drawing a black ball is 1/4 or 0.25.

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