The question is incomplete. So, the complete question is:
For each of the following situations, state the probability rule or rules that you would use and apply it or them. Write a sentence explaining how the situation illustartes the use of the probability rules. (a) The Probability of event A is 0.417. What is the probability that even A does not occur? (b) A coin is tossed 4 times. The probability of zero heads is 1/16 and the probability of zero tails is 1/16. What's the probability that all four tosses result in the same outcomes? (c) Refer to part b, what's the probability that there is at least one head and at least one tail? (d) The probability of event A is 0.4 and the probability of event B is 0.8. Events A and B are disjoint. Can this happen? (e) Event A is rare. Its probability is -0.04. Can this happen?
Answer and Explanation:
(a) P(A)=0.417
Since it's wanted to known the probability of not occuring,
P(A') = 1 - P(A)
P(A') = 1 - 0.417
P(A') = 0.583
The probability of event A not occuring is 0.583.
(b) If the coin is fair, the probability of either head or tail is 1/2. Since, there were 4 tosses, the probability for total outcomes would be 1/16.
For all heads: P(H) = 1/16;
For all tail: P(T) = 1/16:
As it wants "either all heads OR all tails", it will be
P = P(H)+P(T)
P = 1/16+1/16
P = 1/8 = 0.125
The probability of all heads or all tails is 0.125.
(c) The probability of at least one head or one tail is the probability of NOT being all heads and all tails, so:
1 - 0.125 = 0.875
The probability of at least one of each is 0.875.
(d) Yes, events A and B can be disjoint if their intersection is zero:
P(A∩B) = 0 and it also means the events are mutually exclusive.
(e) No, probability can not be negative, because an event has to occur to calculate probability and a set of numbers fo the event is positive.
