You and your friend decide to get your cars inspected. You are informed that 70% of cars pass inspection. If the event of your car’s passing is independent of your friend’s car:
iii. What is the probability that both of the cars pass inspection (6 points)?
a. 60% b. 49% c. 70%
Real estate ads suggest that 65% of homes for sale have garages, 20% have swimming pools, and 18% have both features. What is the probability that a home for sale has: iii. A pool but no garage (6 points)? a. 15% b. 4% c. 2%
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
.70 * .70 = ?
I got 2 percent for number two. But I can't solve for number one. Is it 60%?
0.43
To find the probability in both scenarios, we can use the concept of independent events.
For the first scenario, let's denote the probability of your car passing the inspection as P(your car passes) = 0.70. Since the events are independent, the probability of your friend's car passing is also P(friend's car passes) = 0.70.
To find the probability that both cars pass inspection, we multiply the individual probabilities:
P(both cars pass) = P(your car passes) x P(friend's car passes)
= 0.70 x 0.70
= 0.49
Therefore, the probability that both cars pass inspection is 49%.
For the second scenario, let's denote the probability of a home having a garage as P(garage) = 0.65 and the probability of a home having a swimming pool as P(pool) = 0.20. The probability of a home having both features is given as P(garage and pool) = 0.18.
To find the probability that a home has a pool but no garage, we need to subtract the probability of having both features from the probability of having only a pool:
P(pool but no garage) = P(pool) - P(garage and pool)
= 0.20 - 0.18
= 0.02
Therefore, the probability that a home for sale has a pool but no garage is 2%.
So, the answers to the questions are:
iii. For the car inspection scenario, the probability that both cars pass inspection is c. 70%.
iii. For the real estate scenario, the probability that a home for sale has a pool but no garage is c. 2%.