Mr. Spark has problems starting his two cars during the winter. He decided to record the number of times each car starts during a 30-day period. He recorded the following information. His Hyundai started 18 times. His Subaru started 20 times. Both cars started 40% of the time.
What is the probability that, on any particular morning during a 30-day period,
a.) at least one car started?
b.)neither car started?
To find the probabilities for each scenario, we need to calculate the probabilities using the recorded information.
a) Probability that at least one car started:
To find this probability, we will calculate the probability that neither car starts and subtract it from 1.
Probability neither car starts = (1 - Probability Hyundai starts) * (1 - Probability Subaru starts)
Given that both cars started 40% of the time, the probability that any particular car starts is 40% or 0.4.
Probability neither car starts = (1 - 0.4) * (1 - 0.4) = 0.6 * 0.6 = 0.36
Probability at least one car starts = 1 - Probability neither car starts = 1 - 0.36 = 0.64
So, the probability that at least one car started on any particular morning during a 30-day period is 0.64, or 64%.
b) Probability that neither car started:
The probability that neither car starts is the product of the individual probabilities that each car doesn't start.
Probability neither car starts = (1 - Probability Hyundai starts) * (1 - Probability Subaru starts)
Probability neither car starts = (1 - 0.4) * (1 - 0.4) = 0.6 * 0.6 = 0.36
So, the probability that neither car started on any particular morning during a 30-day period is 0.36, or 36%.
To find the probability, we first need to calculate the probability of each event happening and then use those probabilities to find the answer.
a.) To find the probability that at least one car started, we need to calculate the probability that neither car started and subtract it from 1. We are given that both cars started 40% of the time, which means that they did not start 60% of the time.
The probability that neither car started is calculated as follows:
Probability of neither car starting = (Probability of Hyundai not starting) x (Probability of Subaru not starting)
Since the cars started 40% of the time, they did not start 60% of the time. Therefore:
Probability of neither car starting = 0.6 x 0.6 = 0.36
Now, we subtract this probability from 1 to find the probability that at least one car started:
Probability of at least one car starting = 1 - Probability of neither car starting
Probability of at least one car starting = 1 - 0.36
Probability of at least one car starting = 0.64
Therefore, the probability that on any particular morning during a 30-day period at least one car started is 0.64 or 64%.
b.) To find the probability that neither car started, we already calculated it as 0.36 in the previous step. Therefore, the probability that on any particular morning during a 30-day period neither car started is 0.36 or 36%.