A box contains 10 ​transistors,4 of which are defective. If 4 are selected at​ random, find the probability that

a. All are defective.
b. None are defective.

a. All are defective.

Well, since there are 10 transistors in total and 4 of them are defective, the probability of selecting a defective transistor on the first draw is 4/10.

Now, when we pick the second transistor, there are only 9 left in the box and only 3 defective ones, so the probability of selecting a defective transistor on the second draw is 3/9.

Similarly, for the third draw, the probability is 2/8, and for the fourth draw, it is 1/7.

To find the probability that all four transistors are defective, we multiply these probabilities together:
(4/10) * (3/9) * (2/8) * (1/7) = 1/210

So, the probability that all four transistors are defective is 1/210.

b. None are defective.
Now, the probability of picking a non-defective transistor on the first draw is 6/10, since there are 6 non-defective out of the total 10 transistors.

For the second draw, there are 5 non-defective transistors left out of the remaining 9, so the probability is 5/9.

For the third draw, the probability is 4/8, and for the fourth draw, it is 3/7.

To find the probability that none of the four transistors are defective, we multiply these probabilities together:
(6/10) * (5/9) * (4/8) * (3/7) = 1/14

So, the probability that none of the four transistors are defective is 1/14.

Remember, these probabilities assume that the transistors are being chosen randomly, so make sure to mix them up well!

To find the probability in each case, we need to use the concept of combinations.

a. Probability that all 4 transistors are defective:
In this case, we need to select all 4 defective transistors from the 4 defective ones available.

Number of ways to select 4 defective transistors = 4C4 = 1
Total number of ways to select 4 transistors from 10 available = 10C4

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / (10C4)

b. Probability that none of the transistors are defective:
In this case, we need to select all 4 transistors from the 6 non-defective ones available.

Number of ways to select 4 non-defective transistors = 6C4
Total number of ways to select 4 transistors from 10 available = 10C4

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 6C4 / 10C4

Now, we can calculate the probabilities using the above formulas.

To find the probability in each case, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

a. Probability that all selected transistors are defective:
To find the probability that all selected transistors are defective, we need to select all 4 defective transistors from the 4 available in the box.

Total number of possible outcomes: We need to select 4 transistors from a total of 10 transistors, so we can use the combination formula:
Number of possible outcomes = 10C4 = 210

Number of favorable outcomes: We need to select all 4 defective transistors from the 4 defective ones in the box, so we can use the combination formula:
Number of favorable outcomes = 4C4 = 1

Probability = Number of favorable outcomes / Number of possible outcomes = 1 / 210

b. Probability that none of the selected transistors are defective:
To find the probability that none of the selected transistors are defective, we need to select 4 working (non-defective) transistors from the 6 available in the box.

Total number of possible outcomes: We need to select 4 transistors from a total of 10 transistors, so we can use the combination formula:
Number of possible outcomes = 10C4 = 210

Number of favorable outcomes: We need to select 4 working (non-defective) transistors from the 6 non-defective ones in the box, so we can use the combination formula:
Number of favorable outcomes = 6C4 = 15

Probability = Number of favorable outcomes / Number of possible outcomes = 15 / 210

Therefore,
a. The probability that all 4 selected transistors are defective is 1/210.
b. The probability that none of the selected transistors are defective is 15/210.

first one:

4/10
second one
3/9
third one
2/8
fourth one
1/7
now multiply :)
------------------------
ow all good
first one
6/10
second one
5/9
etc