Since the sum of the probabilities of all possible outcomes must be 100%, we can deduce the following:
- Cooking in under 20 minutes: 10%
- Cooking between 20 and 30 minutes: 85%
- Cooking in more than 30 minutes: 5%
In fact, the probabilities of cooking in less than 20 or more than 30 sum up to 15%, which means that the remaining outcome (i.e. cooking time between 20 and 30) must complete this probability to 15, and in fact 15+85=100.
That being said, all three answers are simply a combination of these three scenarios: let C be the cooking time, for aesthetic reasons:
[tex]P(C\geq 20) = P(20 \leq C \leq 30)+P(C\geq30) = 85\%+5\%=90\%[/tex]
[tex]P(20 \leq C \leq 30) = 85\%[/tex]
[tex]P(C\leq 30) = P(C\leq20)+P(20 \leq C \leq 30) = 10\%+85\%=95\%[/tex]
