A batch consists of 2 defective coils and 48 good ones. Find the probability of getting no defective coils when three coils are randomly selected without replacement
To find the probability of getting no defective coils when three coils are randomly selected without replacement, we need to use the concept of combinations and multiply the probabilities of individual events.
Step 1: Find the total number of ways to select 3 coils from the given batch
When selecting without replacement, we use combinations, since the order does not matter. The formula for combinations is:
nCk = n! / (k! * (n-k)!)
where n is the total number of items and k is the number of items to be selected.
In this case, the total number of coils is 50 (2 defective + 48 good). So, the number of ways to select 3 coils from a batch of 50 coils is:
50C3 = 50! / (3! * (50-3)!)
Step 2: Find the number of ways to select 3 good coils from the given batch
Since there are 48 good coils in the batch, we need to calculate 48C3, which represents the number of ways to select 3 good coils from 48.
48C3 = 48! / (3! * (48-3)!).
Step 3: Find the probability of getting no defective coils
To calculate the probability, we divide the number of favorable outcomes (no defective coils) by the total number of possible outcomes (any 3 coils selected).
The probability of getting no defective coils = (48C3) / (50C3).
Now you can calculate the probability using the formulas given above.
To find the probability of getting no defective coils when three coils are randomly selected without replacement, we can use the concept of combinations.
First, let's find the total number of ways to select 3 coils out of the batch of 50 (48 good ones and 2 defective ones). This can be done using combinations.
The total number of ways to select 3 coils out of 50 can be calculated as:
C(50, 3) = 50! / (3! * (50-3)!)
= 50! / (3! * 47!)
= (50 * 49 * 48) / (3 * 2 * 1)
= 19600
Now, let's find the number of ways to select 3 good coils out of the 48 available. This can be calculated using combinations as well:
C(48, 3) = 48! / (3! * (48-3)!)
= 48! / (3! * 45!)
= (48 * 47 * 46) / (3 * 2 * 1)
= 17296
Finally, to find the probability of getting no defective coils, we divide the number of favorable outcomes (getting 3 good coils) by the total number of possible outcomes:
P(no defective coils) = number of favorable outcomes / total number of outcomes
= 17296 / 19600
≈ 0.8833 (rounded to four decimal places)
Therefore, the probability of getting no defective coils when three coils are randomly selected without replacement is approximately 0.8833.