1.) In a certain large city, 23% of cars are purple. If you pick a car in this c
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Question
1.) In a certain large city, 23% of cars are purple. If you pick a car in this city at random, what is the probability that you do NOT get a purple car?
2.) In a certain large city, 23% of cars are purple. This is a very large city. If we pick one car at random and set it aside, the rest of the cars are still 23% purple. Even if we pick two or three cars and set them aside, the rest of the cars are still 23% purple. If we choose three cars at random, the cars are ‘independent’ of each other. Probability for all three cars is therefore probability for each car, multiplied together. What is the probability that all three randomly chosen cars are purple? PERCENT ANSWER, TWO PLACES AFTER THE DECIMAL.
Explanation / Answer
1) % of purple cars= 23%
Probability of picking a purple car at random = 23/100 =0.23
% of non-purple cars = 100 - 23 = 77%
Probability of picking a non-purple car at random = 77/100 = 0.77
2) As explained, despite being picking cars without replacement, the count of the cars is so huge that replacement does not influence the probability. And acts as if the cars are picked with replacement.
Probablity of 1st car being purple = 0.23
Because of the above stated condition, the probability of 2nd and 3rd cars = 0.23 & 0.23 as well.
Therefore, probability that all random chosen cars are purple = 0.23 * 0.23 *0.23
= 0.012167 = 1.2167% ~ 1.22%
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