Question

a package contains 9 resistor 2 of which are defective find the probability of

0 being defective

1 being defective

2 being defective

3 being defective

Answer #1

Let X be a random variable representing the number of defective resistors in the package. Then X is a binomial random variable with n=9 and p=2/9.

We know

Then the probability of 0 being defective is

Then the probability of 1 being defective is

Then the probability of 2 being defective is

Then the probability of 3 being defective is

A package contains 10 resistors, 2 of which are defective. If 2
resistors are selected at random without replacement, find the
probability of getting at least one defective.

A package contains 4 light bulbs. The following table gives the
probability distribution (pdf) of the number of broken bulbs in the
package. A random package is selected. Use the table to answer the
following questions:
pdf for DRV
X
0
1
2
3
4
p(x)
0.66
0.20
?
0.05
0.02
What is the probability that there are exactly 2 defective
bulbs in a package?
What is the probability that there are at most 2 defective
bulbs in a package?...

A manufactured parts is defective with probability 1/2 and being
defective or not is independent among all the parts. Bin A consists
of n + 1 parts and bin B consists of n parts. What is the
probability that bin A consists of more defectives than bin B?

A box contains 7 items, 4 of which are defective. a random
sample of 3 items are taken from the box. Let X be the number of
defective items in the sample. 1.Find the probability mass function
of X. 2.Find the mean and the variance of X.

Electric switches are shipped in packages of 12 items. The
probability that an item is defective is 0.15. What is the
probability that one package contains: (a) at least one defective
switch; (b) more than one defective switch. (c) If the shipper
decides to compensate the buyer for the defective switches by
paying $2 for each defective switch, what is the expected
compensation amount for each package of 12 items?

A box contains 100 light bulbs of which 22 are defective.
Suppose 2 light bulbs are selected without replacement.
What is the probability that at least one of them is defective?
Give your answer to 3 places past the decimal.

Q‒2. [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.
Find the transitive closure of if is
a) .
b) .

A box contains 25 parts of which 3 are defective and 22
are non-defective. If two parts are selected WITH replacement, find
the following probabilities;
P (both are defective) =
P ( exactly one is defective) =
P ( neither is defective) =

A munitions warehouse contains 50 bombs, of which 3 are
defective (6%). A sample of 10 bombs is drawn and tested. What is
the probability that the sample will contain at most 1 defective
bomb?

2) The probability of any car being defective in the products of
a car company is 0.1 is known as. If 200 vehicles are chosen
randomly from this company, the number of defective cars,
a) At least 25
b) up to 18
c) Between 15 and 28
what is this possibility?

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