I have two questions which i need some help and tell me what is wrong with my attempted answers:
A box contains 100 items, 2 of which are faulty. If 2 are selected at random without replacement calculate the probabilities that 0, 1 or 2 of the selected items are faulty.
This my attempt for the first probaility:
Pr(0 Faulty)= (99/100) * (98/100)
An electronic components manufacturer submits tenders to three separate companies for a work over the next month. From past experience the contracts manager estimates that the probability that each tender will be accepted as in the table below.
Company Probability
A 0.8
B 0.6
C 0.9
Calculate the probability that at least one tender is accepted:
This is my attempt:
I have assumed this is independent.
Pr(at least one tender) = Pr(A) + Pr(B) + Pr(C) + Pr(A U B) + Pr(A U C) + Pr(B U C) + Pr(A U B U C)
P.S
This can't be right. There are 100 items but 2 are faulty so there are 98, out of 100, that are not. The probabilty that the first your draw is not faulty is 98/100, not 99/100. Also, because this is sampling without replacement, you now have 97 non-faulty out of 99 total. The probability that the second is also not faulty is 97/99.
To draw "one faulty" you can either draw first a good one and then a bad one or vice versa. The probability that the first you draw is not faulty is, again, 98/100. You now have two faulty ones out of 99 total so the probabilty that the second drawn is faulty is 2/99. Doing it the other way, the probabilty that the first you draw is faulty is 2/100 and then the probability that the second is not is 98/99. Of course,
so the order really doesn't matter. The probability of drawing one faulty item is .
The probability that the first you draw is faulty is and then the probability that the second is also is . The probability that both are faulty is .
That doesn't look like a very good method- too complicated.An electronic components manufacturer submits tenders to three separate companies for a work over the next month. From past experience the contracts manager estimates that the probability that each tender will be accepted as in the table below.
Company Probability
A 0.8
B 0.6
C 0.9
Calculate the probability that at least one tender is accepted:
This is my attempt:
I have assumed this is independent.
Pr(at least one tender) = Pr(A) + Pr(B) + Pr(C) + Pr(A U B) + Pr(A U C) + Pr(B U C) + Pr(A U B U C)
P.S
"At least one" is the same as "NOT none". Calculate the probability that NO tender is accepted (and, of course the probabilities that offers to A, B, and C separately are NOT accepted are 1- .8= .2, 1- .6= .4, and 1- .9= .1, respectively) and subtract from 1. Assuming that these are independent, just multiply the probabilities.
Paymemoney,
Your question makes me suspect that you are not familiar with the notation used by Plato.
In this context,
is not a matrix; it is a binomial coefficient, or equivalently, the number of ways to choose m items out of a set of n objects. So
For example,
Does that help?