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Chapter 8: Problem 416

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 \(\frac{4}{16}\).

Step by step solution

01

Calculate total number of balls

To calculate the probability, we first need to find out the total number of balls present in the box. The box contains 7 red, 5 white, and 4 black balls. Total balls = Red balls + White balls + Black balls Total balls = \(7+5+4\)
02

Calculate the probability of drawing a red ball

Now, we will find the probability of drawing a red ball. The probability is calculated as the ratio of the number of desired outcomes to the total number of outcomes. Probability of drawing a red ball = \(\frac{Number \ of \ red \ balls}{Total \ number \ of \ balls}\) Probability of drawing a red ball = \(\frac{7}{7+5+4}\)
03

Calculate the probability of drawing a black ball

Similarly, we can find the probability of drawing a black ball. Probability of drawing a black ball = \(\frac{Number \ of \ black \ balls}{Total \ number \ of \ balls}\) Probability of drawing a black ball = \(\frac{4}{7+5+4}\) Now we have calculated the probabilities for both a red and black ball. The answer is the Probability of drawing a red ball and Probability of drawing a black ball.

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Most popular questions from this chapter

A die is tossed five times. What is the probability that an ace will appear: (a) at least twice; (b) at least once?

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