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.
A lot of 1000 screws contains 30 that are defective. Two are
selected at random, without replacement, from the lot. Let A and B
denote the events that the first and second screws are defective,
respectively.
(a) Prove whether or not A and B are independent events using
mathematical expressions of probability.
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 day’s production of 850 parts contains 50 defective parts.
Three parts are selected at random without replacement. Let the
random variable ? equal the number of defective parts in the
sample.
1. Find the probability mass function
2. Find the cumulative distribution function of ?.
3. Find ?(? > 0.5) =
4. Find ?(1.5) =
5. Find ?(2) − ?(0.3) =
6. Find ?(0.99 < ? < 2.5) =
A shipment contains 200 items of which 50 are defective. A sample of 16 items from the shipment is selected at random without replacement. We accept the shipment if at most 3 items in the sample are defective. (a) Write down (but do not evaluate) an exact formula for the probability of acceptance. (b) Use a Table to give the decimal value for the binomial approximation of the probability of acceptance. Show your work. (c) Suppose instead that the shipment contains 500 items of...
Suppose that a bag contains 16 items of which 8 are defective.
Four items are selected at random without replacement. Find the
probabilities that:
Provide your answers in 2 d.p (decimal point) without space in
between the values
only one item is defective
all selected items are non-defective
all selected items are defective
at least one of the selected items is defective
1) 4 ballpoint pens are selected without replacement
at random from a box that contains 2 blue pens, 3 red pens, and 5
green pens.
If X is the number of blue pens selected and Y is the number of red
pens selected
a. Write the “joint probability distribution” of x and
y.
b. Find P[(X, Y ) ∈ A], where A is the region
{(x, y)|x + y ≤ 2}.
c. Show that the column and row totals of...
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 shipment of 6 television sets contains 2 defective sets. A
hotel makes a random purchase of 3 of the sets. If x is the number
of defective sets purchased by the hotel, find the cumulative
distribution function of the random variable X representing the
number of defective. Then using F(x), find
(a)P(X= 1) ;
(b)P(0< X≤2).
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.