A car manufacturer produces only red and blue TCS Models which come out of the…
2024
A car manufacturer produces only red and blue TCS Models which come out of the final testing area at random. What are the odds that five consecutive cars of same color will come through the test area at any one time?
- A.
1/25
- B.
1/125
- C.
1/32
- D.
1/16
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Correct answer: D
Each car's color is independent and can be red or blue with equal probability 1/2.
For five cars, the probability that they are all red is (1/2)^5 = 1/32.
Similarly, the probability that they are all blue is also (1/2)^5 = 1/32.
The events "all red" and "all blue" are mutually exclusive, so the probability that all five cars are the same color is 1/32 + 1/32 = 2/32 = 1/16.
Therefore, the probability that five consecutive cars are of the same color is 1/16.