2.51 Find the errors in each of the following state- ments (a) The probabilities

Question

2.51 Find the errors in each of the following state- ments (a) The probabilities that an automobile salesperson will sell 0, 1, 2, or 3 cars on any given day in Febru ary are, respectively, 0.19, 0.38, 0.29, and 0.15. (b) The probability that it will rain tomorrow is 0.40 and the probability that it will not rain tomorrow is 0.52. (c) The probabilities that a printer will make 0, 1, 2, 3, or 4 or more mistakes in setting a document are, respectively, 0.19,0.34, -0.25,0.43, and 0.29. (d) On a single draw from a deck of playing cards the probability of selecting a heart is 1/4, the probabil- ity of selecting a black card is 1/2, and the proba- bility of selecting both a heart and a black card i:s 1/8.

Explanation / Answer

1. the net probability should add upto 1, but 0.19 + 0.38 + 0.29 + 0.15 = 1.01 >1

Total probabilities sum to greater than 1.0 which is not possible, as they are mutually exclusive.

2. there are only 2 options, either it will rain or it will not , so

P(rain) + P(not rain) = 1

but, P(rain) + P(not rain) = 0.20 + 0.52 = 0.72 <1

The sum of the two probabilities are 0.72 total. It should sum to 1.00, as the two events are the only possible outcomes.

3.Probability can never be neagtive, -0.25. You cannot have a negative probability.

4. The probability of selecting both a heart and black card = 0 , there are no black hearts

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