Question

I. A coin is tossed four times. The probability is ¼ or 0. 25 that all four tosses will result in a head face up. Ii. A coin is tossed four times. The probability is 1/8 or 0. 125 that all four tosses will result in a head face up. Iii. If two events are mutually exclusive, then P(A or B) = P(A)P(B). (i), (ii) and (iii) are all correct statements. (i) and, (ii) are correct statements but not (iii). (i) and, (iii) are correct statements but not (ii). (ii) and, (iii) are correct statements but not (i)

Answer 1

The correct answer is (ii) and (iii) are correct statements but not (i).

Step-by-step explanation:

(i) states that the probability of getting four heads in four tosses of a coin is 1/4 or 0.25, which is incorrect. The probability of getting four heads in four tosses of a fair coin is (1/2)^4 = 1/16 = 0.0625.

(ii) states that the probability of getting four heads in four tosses of a coin is 1/8 or 0.125, which is correct. The probability of getting four heads in four tosses of a fair coin is (1/2)^4 = 1/16 = 0.0625, which is equal to 1/8.

(iii) is a correct statement and is known as the addition rule for mutually exclusive events. It states that if two events A and B are mutually exclusive, meaning that they cannot occur at the same time, then the probability of either A or B occurring is equal to the sum of their individual probabilities, i.e., P(A or B) = P(A) + P(B).