P(27chose 2) (43 choose 2)
27/43 * 26/42 = 702/1806 = .3887
Round to four decimal places.
27/43 * 26/42 = 702/1806 = .3887
First, let's find the number of possible outcomes. We are selecting 2 cars from a total of 43 cars, so the total number of possible outcomes is given by the combination formula:
C(43, 2) = 43! / (2!(43-2)!) = 43! / (2!41!) = (43 * 42) / (2 * 1) = 903.
Next, let's find the number of favorable outcomes. Since there are 27 cars with GPS systems, the number of favorable outcomes is given by selecting 2 cars from these 27:
C(27, 2) = 27! / (2!(27-2)!) = 27! / (2!25!) = (27 * 26) / (2 * 1) = 351.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
P(both cars have GPS systems) = 351 / 903 ≈ 0.3883 (rounded to four decimal places).
Therefore, the probability that both selected cars have GPS navigation systems is approximately 0.3883.