Question

In: Math

A box has 11 parts of which 4 are defective and 7 acceptable. 2 parts are...

A box has 11 parts of which 4 are defective and 7 acceptable. 2 parts are chosen at random without replacement. Find the probability that:

a) both parts are defective.

b) both parts are acceptable.

c) only one part is defective.

Expert Solution

Box has 4 defective parts and 7 acceptable parts

a) Probability of picking a defective part in first pick = 4/11

Probability of picking a defective part in second pick = 3/10 since 1 defective part was already picked

Therefore probability of picking both defective parts = (4/11)*(3/10) = 6/55 = 0.1091

b) Probability of picking an acceptable part in first pick = 7/11

Probability of picking an acceptable part in second pick = 6/10 since 1 acceptable part was already picked

Therefore probability of picking both acceptable parts = (7/11)*(6/10) = 21/55 = 0.3818

c) Case 1:

Probability of picking an acceptable part in first pick = 7/11

Probability of picking a defective part in second pick = 4/10

Case 2:

Probability of picking a defective part in first pick = 4/11

Probability of picking an acceptable part in second pick = 7/10

Therefore probability of picking only one defective part = (7/11)*(4/10) +(4/11)*(7/10) = 28/55 = 0.5091

milcah answered 1 year ago

Box A contains 7 items of which 2 are defective, and box B contains 6 items of which 1 is defective.

Box A contains 7 items of which 2 are defective, and box B contains 6 items of which 1 is defective. If an item is drawn at random from each box. Find the probability that both items are non- defective. 1/21 19/42 10/13 25/42

A box contains 10 items, of which 3 are defective and 7 are non-defective. Two items...

A box contains 10 items, of which 3 are defective and 7 are non-defective. Two items are randomly selected, one at a time, with replacement, and x is the number of defective items in the sample. To look up the probability of a defective item being drawn from the box, using a binomial probability table, what would be the values of n, x and p to look up?

A box of manufactured items contains 12 items of which 4 are defective. If 3 items...

A box of manufactured items contains 12 items of which 4 are defective. If 3 items are drawn at random without replacement, what is the probability that: 1. The first one is defective and rest are good 2. Exactly one of three is defective

A box contains 12 items, 4 of which are defective. An item is chosen at random and not replaced.

A box contains 12 items, 4 of which are defective. An item is chosen at random and not replaced. This is continued until all four defec- tive items have been selected. The total number of items selected is recorded.

2. Suppose a bin contains 20 manufactured parts and 4 of them are defective. Pick 3...

2. Suppose a bin contains 20 manufactured parts and 4 of them are defective. Pick 3 parts randomly from the bin, with replacement and let X be the number of defective parts picked. Pick parts repeatedly from the bin, with replacement, and let Y be the number of picks until the first defective part is observed. Find the probability mass functions for X and Y . 3. Suppose a bin contains 20 manufactured parts and 4 of them are defective....

4. A bin of 52 manufactured parts contains 13 defective parts. Pick 8 parts from the...

4. A bin of 52 manufactured parts contains 13 defective parts. Pick 8 parts from the bin at random (a) without replacement and (b) with replacement. In each case compute the probability that you get no defective parts. 5. A postcode consists of 5 digits of numbers from 1 to 9. Suppose a postcode is valid if it consists of at least two repeated digits (not real), e.g., 95616 and 96616 are valid but 95617 is not. Suppose one write...

7) A shipment of 10 items contains 4 items which are defective. If we randomly select...

7) A shipment of 10 items contains 4 items which are defective. If we randomly select 4 of the items for inspection, what is the probability of at least 3 non-defective items in the sample? Assume sampling without replacement. a) 185/210 b) 184/210 c) 25/210 d) 115/210* e) 175/210

A box contains 12 items of which 3 are defective. A sample of 3 items is selected from the box

A box contains 12 items of which 3 are defective. A sample of 3 items is selected from the box. Let X denotes the number of defective item in the sample. Find the probability distribution of X.

The percent defective for parts produced by a manufacturing process is targeted at 4%. The process...

The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives. Determine a 88% confidence interval for the proportion defective for the process today. Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer. Place your UPPER limit, rounded to 3 decimal places, in the...

a package contains 9 resistors 2 of which are defective if 4 are selected at random...

a package contains 9 resistors 2 of which are defective if 4 are selected at random find the probability of getting 0 defective 1 defective 2 defective