For each of the following statements, explain in a complete sentence why the sta

Question

For each of the following statements, explain in a complete sentence why the statement is incorrect.

a) City officials have found that the probability that a bus on a certain route is on time is 0.85. Therefore, the probability that it is late is 0.15. b) The probability that a certain investment will decrease in value over a period of one week is 0.27. Therefore, the probability that the stock will increase or stay the same in value is 0.67.

c) A red die and a green die are tossed. The probability that a 6 will appear uppermost on the red die is 1/6 and the probability that a 1 will appear uppermost on the green die is 1/6. Hence, the probability that the red die will show a 6 or the green die will show a 1 is 1/6 + 1/6.

Explanation / Answer

(a) Probability of on time = 0.85.

So, Probability of (1) early and (2) late = 1 - 0.85 = 0.15.

Here, eary is left out.

(b) Probability of decrease = 0.27

Probability of increase or stay the same = 0.67

So, total probability = 0.27 + 0.67= 0.94.

Total probability is not equal to 1.

(c) Let

A = event of red die showing a 6

B = event of green die showing a 1.

By addition theorem of probability:
P(A or B) = P(A) + P(B) - P(A and B).

Only when A and B mutually exclusive:

P(A or B) = P(A) + P(B).

Here, it is not written that the two events A and B are mutually exclusive.

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