Let's break down the question and provide a step-by-step solution for both parts.
### Part (a)
Given:
- The probability that a pupil in a class has a calculator is 0.87.
To find:
- The probability that a pupil does not have a calculator.
Solution:
1. The sum of the probability of all possible outcomes must equal 1. In this case, the two possible outcomes are:
- Having a calculator.
- Not having a calculator.
2. If the probability of having a calculator is 0.87, the probability of not having a calculator is the complement of this probability.
The complement rule states that the probability of an event not occurring is \( 1 \) minus the probability of the event occurring.
[tex]\[
\text{Probability of not having a calculator} = 1 - \text{Probability of having a calculator}
\][/tex]
[tex]\[
\text{Probability of not having a calculator} = 1 - 0.87 = 0.13
\][/tex]
So, the probability that a pupil does not have a calculator is 0.13.
### Part (b)
Given:
- The probability of a football team winning a match is 0.3.
- The probability of the same football team losing a match is 0.55.
To find:
- The probability of the same football team drawing a match.
Solution:
1. Again, the sum of the probability of all possible outcomes must equal 1. In this case, the three possible outcomes are:
- Winning the match.
- Losing the match.
- Drawing the match.
2. If the probability of winning is 0.3 and losing is 0.55, the probability of drawing is the complement of the sum of the probabilities of winning and losing.
[tex]\[
\text{Probability of drawing} = 1 - (\text{Probability of winning} + \text{Probability of losing})
\][/tex]
[tex]\[
\text{Probability of drawing} = 1 - (0.3 + 0.55) = 1 - 0.85 = 0.15
\][/tex]
So, the probability that the football team will draw the match is approximately 0.15.
In conclusion:
- The probability that a pupil does not have a calculator is 0.13.
- The probability that the football team will draw a match is 0.15.
