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Chapter 35: Problem 1108

A bag contains 4 white balls, 6 black balls, 3 red balls, and 8 green balls. If one ball is drawn from the bag, find the probability that it will be either white or green.

Short Answer

Expert verified
The probability of drawing either a white or green ball from the bag is \(\frac{4}{7}\).

Step by step solution

01

Calculate total number of balls

In the bag, we have 4 white balls, 6 black balls, 3 red balls, and 8 green balls. So, the total number of balls in the bag is: Total number of balls = White balls + Black balls + Red balls + Green balls
02

Determine desirable number of balls

We want to find the probability of drawing either a white ball or a green ball. Thus, we will consider white and green balls as our desirable outcomes. The total number of desirable balls in the bag is: Total desirable balls = White balls + Green balls
03

Calculate probability using the formula

Now we will use the probability formula, which is: Probability = Total desirable balls / Total number of balls Let's calculate the probability.
04

Calculate the total number of balls and desirable balls

Total number of balls = 4 white balls + 6 black balls + 3 red balls + 8 green balls = \((4 + 6 + 3 + 8)\) balls = 21 balls Total desirable balls = 4 white balls + 8 green balls = \((4 + 8)\) balls = 12 balls
05

Calculate the probability of drawing a white or green ball

Now we can use the formula from step 3: Probability = Total desirable balls / Total number of balls Probability = 12 balls / 21 balls = \(\frac{12}{21}\)
06

Simplify the probability fraction

Both the numerator and the denominator are divisible by 3, so let's simplify the fraction: \[\frac{12}{21} = \frac{12 \div 3}{21 \div 3} = \frac{4}{7}\] The probability of drawing a white or green ball is \(\frac{4}{7}\).

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