Statistics Binomial Distribution Question?

Question

82% of items are regular and 77% of regular items are of the top quality. What is the probability that a randomly picked regular item is of the top quality?

Please show all work!

I copied the question exactly as it appears, but I suspect that it should be 'a randomly picked item'.

Answer 1

If 77% of regular items are of the top quality, what is the probability that a randomly picked regular item is of the top quality? 77%, of course.

But I suspect that the value you want is the probability that a randomly picked item (not a REGULAR item) is of the top quality? (Check whether you copied the problem correctly.

Assuming that is the case, Socrates says:

- If 82% of 10,000 items are regular? How many items are regular? (You'll have to do a multiplication.)
- Of those regular items, if 77% are of top quality, how many are top quality? (You'll have to do another multiplication.)
- If that many are top quality out of the total 10,000 items, what percentage of the 10,000 are top quality? (You'll have to do a division problem and express the answer as a percentage.)
- If that percentage of the total items are top quality, what is the probability that a randomly picked item is of the top quality? (Should be obvious.)

Please show all work.

Answer 2

What is the probability that a randomly picked item is top quality given that it's regular?

P( Top given regular) = P(top and regular)/P(regular)

= .77 /..82 = .939

Answer 3

from the way you worded it, it sounds like it's a 77% chance that a randonly picked regular item is of top quality.

if you want to pick a random item and find the probablity that the item is both regular and of top quality then just mutiply

.82*.77=.6314
63.14%

Answer 4

P(a|b)=p(ab)/p(b)
where a is the event of an item being regular, b is event of an item being of top quality
p(a|b)=0.77/0.82=0.939