Question

(i) if there is absolutely no chance a person will purchase a new car this year, the probability assigned to this event is zero. (ii) if the set of events are collectively exhaustive and mutually exclusive, the sum of the probabilities equals 1. (iii) suppose four heads did appear face up on the toss of a coin four times. the probability that a head will appear face up in the next toss of the coin is 1/2 or 0.5. a. (i), (ii) and (iii) are all false statements. b. (i) is a correct statement but not (ii) or (iii). c. (ii) and, (iii) are correct statements but not (i). d. (i), (ii) and (iii) are all correct statements e. (i) and, (iii) are correct statements but not (ii).

Explanation:

• (i) An impossible event has a probability of 0, so this is correct.
• (ii) Collectively exhaustive events cover all possible outcomes, and mutually exclusive events have no overlap; their total probability sums to 1, so this is correct.
• (iii) Coin tosses are independent, so the prior results do not affect the next toss; the probability of heads remains 0.5, so this is correct.

Answer:

d. (i), (ii) and (iii) are all correct statements