Question
There are 14 red balls,4 white balls, and 10 blue balls in a box.A ball is selected at random from the box. (a).find the probability that the ball is either blue or red (b).find the probability that the ball is neither red nor white
Answers
GPT-4o mini
To solve the problem, let's first summarize the total number of balls in the box:
- Red balls: 14
- White balls: 4
- Blue balls: 10
Now, we can calculate the total number of balls:
\[
\text{Total number of balls} = 14 \, (\text{red}) + 4 \, (\text{white}) + 10 \, (\text{blue}) = 28
\]
### (a) Probability that the ball is either blue or red
To find the probability that a ball is either blue or red, we first need to find the total number of blue and red balls:
\[
\text{Number of blue or red balls} = \text{Number of red balls} + \text{Number of blue balls} = 14 + 10 = 24
\]
Now we can calculate the probability:
\[
P(\text{blue or red}) = \frac{\text{Number of blue or red balls}}{\text{Total number of balls}} = \frac{24}{28}
\]
To simplify this fraction, we can divide the numerator and denominator by 4:
\[
P(\text{blue or red}) = \frac{24 \div 4}{28 \div 4} = \frac{6}{7}
\]
### (b) Probability that the ball is neither red nor white
To find the probability that a ball is neither red nor white, we only consider the blue balls. The number of blue balls is 10, as there are 0 other colors that fit this description.
\[
P(\text{neither red nor white}) = \frac{\text{Number of blue balls}}{\text{Total number of balls}} = \frac{10}{28}
\]
Again, we can simplify this fraction by dividing the numerator and denominator by 2:
\[
P(\text{neither red nor white}) = \frac{10 \div 2}{28 \div 2} = \frac{5}{14}
\]
### Final Answers
(a) The probability that the ball is either blue or red is \(\frac{6}{7}\).
(b) The probability that the ball is neither red nor white is \(\frac{5}{14}\).
- Red balls: 14
- White balls: 4
- Blue balls: 10
Now, we can calculate the total number of balls:
\[
\text{Total number of balls} = 14 \, (\text{red}) + 4 \, (\text{white}) + 10 \, (\text{blue}) = 28
\]
### (a) Probability that the ball is either blue or red
To find the probability that a ball is either blue or red, we first need to find the total number of blue and red balls:
\[
\text{Number of blue or red balls} = \text{Number of red balls} + \text{Number of blue balls} = 14 + 10 = 24
\]
Now we can calculate the probability:
\[
P(\text{blue or red}) = \frac{\text{Number of blue or red balls}}{\text{Total number of balls}} = \frac{24}{28}
\]
To simplify this fraction, we can divide the numerator and denominator by 4:
\[
P(\text{blue or red}) = \frac{24 \div 4}{28 \div 4} = \frac{6}{7}
\]
### (b) Probability that the ball is neither red nor white
To find the probability that a ball is neither red nor white, we only consider the blue balls. The number of blue balls is 10, as there are 0 other colors that fit this description.
\[
P(\text{neither red nor white}) = \frac{\text{Number of blue balls}}{\text{Total number of balls}} = \frac{10}{28}
\]
Again, we can simplify this fraction by dividing the numerator and denominator by 2:
\[
P(\text{neither red nor white}) = \frac{10 \div 2}{28 \div 2} = \frac{5}{14}
\]
### Final Answers
(a) The probability that the ball is either blue or red is \(\frac{6}{7}\).
(b) The probability that the ball is neither red nor white is \(\frac{5}{14}\).