4. General: Valid Probabilities

(a) Explain why –0.41 cannot be the probability of some event.

Solution: Probability is a positive measure, going from 0 to 1 which indicates the likelihood of occurrence of events. Therefore, it cannot take the value -0.41, because it doesn’t belong to the interval [0, 1].

(b) Explain Why 1.21 cannot be the probability of some event.

Solution: Same reason as above, the probability takes values on the interval [0, 1], therefore 1.21 cannot be a probability.

(c) Explain why 120% cannot be the probability of some event.

Solution: Another way to interpret probability is to associate a percentage (%) to a given probability on the range [0, 1], multiplying is by 100. For instance, a probability of 0.4 is associated with a 40% probability. But the percentages go from 0% to 100% and not beyond. Therefore, 120% can not be a probability.

(d) Can the number 0.56 be the probability of an event? Explain.

Solution: Certainly. Assume we have a closed bag (you cannot see inside) and you have 56 white balls, and 44 black balls. Then you pick one ball randomly. The probability of getting a white one is 0.56.