Problem 1BSC

Calculating Probabilities Based on a Saint Index survey, assume that when adults are asked to identify the most unpopular projects for their hometown, 54% include Wal-Mart among their choices. Suppose we want to find the probability that when five adults are randomly selected, exactly two of them include Wal-Mart. What is wrong with using the multiplication rule to find the probability of getting two adults who include Wal-Mart followed by three people who do not include Wal-Mart, as in this calculation: (0.54)(0.54)(0.46)(0.46)(0.46)?

Solution 1BSC

It is given that, 54% of adults included Walmart as one of the unpopular projects. Suppose 5 adults are randomly selected, then, the probability of getting exactly two adults who include WalMart can be calculated using Binomial distribution probability function.

To calculate the above probability, once should consider all combinations of

The calculation in Binomial formula includes all combinations of 5 arrangements =10 in which two are favorable cases. Here, the given calculation is only one particular case of all the 10 combinations.

Since the given sequence of values does not include all combinations, the given calculation is wrong.