If 67% of cars have automatic tranny's & 8 cars are selected at random what is the probability that fewer than 4 have an automatic tranny
To find the probability of fewer than 4 cars having an automatic transmission (tranny) out of a sample of 8 cars, we need a few steps:
Step 1: Determine the number of ways to choose fewer than 4 cars with an automatic tranny.
Step 2: Determine the number of ways to choose any 8 cars randomly from the given population.
Step 3: Divide the number of favorable outcomes (Step 1) by the total number of outcomes (Step 2) to find the probability.
Let's go through the steps one by one:
Step 1: Determine the number of ways to choose fewer than 4 cars with an automatic tranny.
To calculate this, we need to sum up the possible combinations of selecting 0, 1, 2, and 3 cars with an automatic tranny.
0 cars with automatic tranny: The number of ways to select 0 cars with an automatic tranny is determined by the remaining percentage of cars without an automatic transmission. In this case, it would be 33% (100% - 67%) of the total cars.
Combination: C(8, 0) = 1
1 car with automatic tranny: The number of ways to select 1 car with an automatic tranny can be calculated by selecting 1 car with automatic tranny and 7 cars without an automatic tranny.
Combination: C(8, 1) = 8
2 cars with automatic tranny: The number of ways to select 2 cars with an automatic tranny can be calculated by selecting 2 cars with automatic tranny and 6 cars without an automatic tranny.
Combination: C(8, 2) = 28
3 cars with automatic tranny: The number of ways to select 3 cars with an automatic tranny can be calculated by selecting 3 cars with automatic tranny and 5 cars without an automatic tranny.
Combination: C(8, 3) = 56
Now, summing up the combinations:
Total number of favorable outcomes = C(8, 0) + C(8, 1) + C(8, 2) + C(8, 3) = 1 + 8 + 28 + 56 = 93
Step 2: Determine the number of ways to choose any 8 cars randomly from the given population.
The total number of ways to choose any 8 cars out of the total population depends on the number of cars available. Since this information is not provided, we cannot determine this value.
Step 3: Calculate the probability.
To find the probability, divide the number of favorable outcomes (Step 1) by the total number of outcomes (Step 2). Without the number of cars available in the population, we cannot determine the exact probability.