Agroup of four components is known to contain two defectives. an inspector tests the components
one at a time until the two defectives are located. once she locates the two defectives, she
stops testing, but the second defective is tested to ensure accuracy. let y denote the number of
the test on which the second defective is found.

a) find the probability distribution for y .
b) if the cost of testing a component is $2 and the cost of repairing a
defective is $4, find the expected total cost for testing and repairing the lot.
c)find the variance for the total cost for testing and repairing of the lot.

a) See below

b) $13.67

c) 0.5555

Step-by-step explanation:

Let us denote with C a correct component and with D a defective one.

We have then the 6 possibilities of arrangement:

a) Find the probability distribution for Y .

P(Y=4) = 3/6 = ½

P(Y=3) = 2/6 = 1/3

P(Y=2) = 1/6

b) If the cost of testing a component is $2 and the cost of repairing a defective is $4, find the expected total cost for testing and repairing the lot.

The expected total cost for testing and repairing the lot is the average of testing and repairing

(5*14 +12)/6 = $13.6666≅ $13.67

c)Find the variance for the total cost for testing and repairing of the lot.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

75

step-by-step explanation:

you do x-29=46 (the number of cantaloupes sold)

in order to find x, you have to find what minus 29 equals 46, meaning you'd have to add 29 to 46.

29+46=75

if you replace x with 75, the equation looks like:

75-29=46

x=75