A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 29 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four decimal places.

47+29 = 76

first one 47/76
second on 46/75
third one 45/74
fourth one 43/73

multiply :)

Well, that's quite the defective situation! Let's see what we can calculate here.

First, the total number of calculators in the group is 47 (defective) + 29 (no defects) = 76.

Now, to find the probability that all four calculators selected are defective, we need to calculate the number of ways to choose four defective calculators out of the total defective calculators and divide it by the number of ways to choose any four calculators out of the total calculators.

The number of ways to choose four defective calculators out of 47 is given by the combination formula: C(47, 4) = 47! / (4! * (47-4)!) = 21,834.

The number of ways to choose any four calculators out of the total 76 is given by the combination formula: C(76, 4) = 76! / (4! * (76-4)!) = 634,946.

So, the probability that all four calculators selected are defective is 21,834 / 634,946 ≈ 0.0344.

Rounding to four decimal places, we get a probability of approximately 0.0344.

Now, please don't let these calculators clown around too much!

To calculate the probability that all four calculators selected are defective, we need to use the concept of probability.

The total number of calculators in the group is 47 (defective) + 29 (no defects) = 76.
Out of these, we need to randomly select 4 calculators.

The probability of selecting a defective calculator on the first selection is 47/76.
The probability of selecting a defective calculator on the second selection is 46/75, as there is now one fewer defective calculator in the group of total calculators to choose from, and the total number of calculators has decreased by one.
Similarly, the probability for the third selection is 45/74.
And the probability for the fourth selection is 44/73.

Now, to find the probability that all four calculators selected are defective, we multiply these probabilities together:

(47/76) * (46/75) * (45/74) * (44/73) ≈ 0.0063 (rounded to four decimal places).

Therefore, the probability that all four calculators selected are defective is approximately 0.0063.

To find the probability that all four calculators selected are defective, we need to consider the total number of ways to select four calculators from the entire group and the number of ways to select four defective ones.

Step 1: Calculate the total number of ways to select 4 calculators from the entire group.
We can use the formula for combinations, which is given by:

C(n, r) = n! / (r!(n - r)!)

where n is the total number of calculators in the group (47 defective + 29 non-defective = 76) and r is the number of calculators being selected (4).

C(76, 4) = 76! / (4!(76 - 4)!)
= 76! / (4!72!)

Step 2: Calculate the number of ways to select 4 defective calculators.
Since we are selecting from the group of 47 defective calculators, the number of ways to select 4 defective calculators can be calculated using the combination formula again:

C(47, 4) = 47! / (4!(47 - 4)!)
= 47! / (4!43!)

Step 3: Calculate the probability.
The probability of selecting all four calculators as defective is the number of ways to select 4 defective calculators divided by the total number of ways to select 4 calculators:

Probability = C(47, 4) / C(76, 4)

Now let's calculate this probability.

Probability = (47! / (4!43!)) / (76! / (4!72!))
= (47! * 4!72!) / (4!43! * 76!)

Round the result to four decimal places to get the final probability.

456