Valentina is investigating potential relationships between hybrid car ownership and the gender of the owner. Assume a survey of 100 persons revealed:
The probability of selecting a person who does not own a hybrid car is 0.315.
If a person does not own a hybrid car, the probability they are female is 0.516.
If a person owns a hybrid, the probability they are male is 0.435.
(You can complete the table below to help you organize the work).
If you were to choose a person at random from the sample, determine the probability they have:
a) A hybrid car.
b) A hybrid car given that they are male.
c) Male gender.
d) A hybrid car or male gender.
e) A hybrid car and male gender.
I'll let you finish:
Let's complete the table, first, GM
One thing to notice is that it's actually easier to imagine 1000 persons sampled.....that will eliminate the decimals (in some cases)
Female Male Total
Hybrid 685 - 298 = 387 685 * .435 ≈ 298 1000 - 315 = 685
Not Hybrid 315* (.516) ≈ 163 315 -163 = 152 315
Total 550 450 1000
a) P ( hybrid car ) = 685/ 1000 = 68.5%
b) P (hybrid given male ) = 298 / 685 = 43.5%
c) P (male) = 450/1000 = 45%
d) P (hybrid or male) = P(hybrid) + P(male) - P(hybrid and male) =
(685 + 450 - 298) /1000 =
837 / 1000 = 83.7%
e) P (hybrid and male) = 298/1000 = 29.8%
Do you see how I got those answers???.....that's the important thing....