question archive 48% of cars in the dealer lot are red, 24% are black, and 11% are white
48% of cars in the dealer lot are red, 24% are black, and 11% are white
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48% of cars in the dealer lot are red, 24% are black, and 11% are white. The reminder is some other specified color. Sales persons randomly show three cars to three different customers. What is the probability the first car shown was red, the second was black, and the third was red again? To be clear the first red car and the second red car maybe the same car. This is called sampling replacement. Use 4 decimal digits.
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Given that, percentage of cars in a dealer lot:
Red cars : 48% => P(Selecting a red car) = 0.48
Black cars : 24% => P(Selecting a black car) = 0.24
White cars : 11% => P(Selecting a white car) = 0.11
Other colored : 100 - (48 + 24 + 11) = 17% => P(Selecting other colored car) = 0.17
Since, replacement is taken into account, even if one car is picked it is replaced and hence the sample size at all times remains the same.
Thus,
X = Instance of picking red car first and then picking a black car and then picking a red car
P(X) = (0.48) * (0.24) * (0.48) = 0.0552
