A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities. [4×5 marks] A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities. a)Exactly 2 are defectives.
b)None is defective.
c)All are defective.
d)At least 1 is defective.

In this exercise we have to use the knowledge of probability to calculate each of the requested probabilities, so we can say that:

a)

b)

c)

d)

a)The probability of the first one being defective is 4/24, and then the probability of the second one being defective is 3/23, because we have one less defective transistor. So the combination will be:

b)So find the not defective, we have:

c)So find the defective, we have:

d)We just need to subtract 100% from the case where all 4 are not defective:

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a) 10.73%

b) 45.60%

c) 0.0094%

d) 54.4%

Step-by-step explanation:

The probability of one transistor being defective is equal the number of defective transistors over the total number of transistors

a)

The probability of the first one being defective is 4/24, and then the probability of the second one being defective is 3/23, because we have one less defective transistor. The probability of the third one being not defective is 20/22, and the fourth one not being defective is 19/21. We also multiply the final probability by a combination of 4 choose 2, because the defective transistors can be any 2 of the group of 4:

C(4,2) = 4! / (2! * 2!) = 6

P = 6 * (4/24) * (3/23) * (20/22) * (19/21) = 0.1073 = 10.73%

b)

Similar to the letter a), we have:

First one not defective: P = 20/24

Second one not defective: P = 19/23

Third one not defective: P = 18/22

Fourth one not defective: P = 17/21

P = (20/24) * (19/23) * (18/22) * (17/21) = 0.4560 = 45.60%

c)

First one defective: P = 4/24

Second one defective: P = 3/23

Third one defective: P = 2/22

Fourth one defective: P = 1/21

P = (4/24) * (3/23) * (2/22) * (1/21) = 0.000094 = 0.0094%

d)

If we want at least 1 defective, we just need to subtract 100% from the case where all 4 are not defective:

P = 1 - 0.4560 = 0.5440 = 54.4%

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

i got 142 as my answer

step-by-step explanation: