A bag contains a total of 30 batteries, of which six are defective. Selecting four at random, without replacement, determine the probability that none of the batteries you select are good.
I think it's 2/15, but im not sure if that's correct....
Prob = (6/30)(5/29)(4/28)(3/27) = 1/1827
oh whoa i was way off! thanks Reiny :)
To determine the probability that none of the batteries you select are good, we can use the concept of combinations.
Step 1: Find the total number of ways to select 4 batteries out of 30.
Since we are selecting without replacement, we can use the combination formula: nCr = n! / ((n - r)! * r!)
In this case, n (the total number of batteries) is 30, and r (the number of batteries being selected) is 4.
So, the total number of ways to select 4 batteries out of 30 is 30C4 = 30! / ((30 - 4)! * 4!)
Step 2: Find the number of ways to select 4 defective batteries out of the 6 defective batteries.
Since we want none of the selected batteries to be good, we need to select all 4 from the 6 defective batteries.
So, the number of ways to select 4 defective batteries out of 6 is 6C4 = 6! / ((6 - 4)! * 4!)
Step 3: Calculate the probability.
The probability of selecting none of the good batteries can be found by dividing the number of favorable outcomes (selecting all 4 defective batteries) by the total number of possible outcomes.
Therefore, the probability is (number of ways to select 4 defective batteries out of 6) / (number of ways to select 4 batteries out of 30).
Now, let's calculate the probability:
Probability = (6C4) / (30C4)
= (6! / ((6 - 4)! * 4!)) / (30! / ((30 - 4)! * 4!))
= (6! * 26!) / (2! * (30! / 26!))
= 6! / 2! * (30 * 29 * 28 * 27)
Calculating this expression gives us the probability that none of the batteries you select are good.