Sure, let's break down the problem step-by-step to find the probabilities for the given events.
First, we need to determine the total number of balls in the box:
- Yellow balls: 4
- Green balls: 6
- Red balls: 8
The total number of balls is:
[tex]\[ 4 + 6 + 8 = 18 \][/tex]
Now let's find the probabilities for each event:
(i) The ball is either yellow or red:
- Number of yellow balls: 4
- Number of red balls: 8
The number of balls that are either yellow or red is:
[tex]\[ 4 + 8 = 12 \][/tex]
The probability of drawing a ball that is either yellow or red is therefore:
[tex]\[ \frac{12}{18} = \frac{2}{3} \][/tex]
This is approximately:
[tex]\[ 0.6667 \][/tex]
(ii) The ball is either green or yellow:
- Number of green balls: 6
- Number of yellow balls: 4
The number of balls that are either green or yellow is:
[tex]\[ 6 + 4 = 10 \][/tex]
The probability of drawing a ball that is either green or yellow is:
[tex]\[ \frac{10}{18} = \frac{5}{9} \][/tex]
This is approximately:
[tex]\[ 0.5556 \][/tex]
(iii) The ball is neither red nor green:
- The only balls that are neither red nor green are the yellow balls. The number of yellow balls is 4.
The probability of drawing a ball that is neither red nor green is:
[tex]\[ \frac{4}{18} = \frac{2}{9} \][/tex]
This is approximately:
[tex]\[ 0.2222 \][/tex]
So, to summarize, the probabilities are:
1. Probability of drawing a ball that is either yellow or red: [tex]\(0.6667\)[/tex]
2. Probability of drawing a ball that is either green or yellow: [tex]\(0.5556\)[/tex]
3. Probability of drawing a ball that is neither red nor green: [tex]\(0.2222\)[/tex]
