Thread: one last question and its doing my head in!

stats. question regards to flavoured milk.

The probability that a flavoured milk container holds more than 500mL of use is 0.2. If a batch of 10 of these milk containers is tested, what is the probability that:
(a) At least half of them will contain more than 500mL?
(b) None of them will contain more than 500mL?

To answer this question you want to think about the possible combinations of containers. In particular (I'll start with (b), as it is the simpler case):

(b) The probability of 500ml (call this event A) is 0.2, which means the probability of <=500ml (call this event B) is (1-0.2)=0.8. So, for this part of the question, you want to consider the probability that all 10 containers have <=500ml, which is the probability associated with 10 instances of event B (hopefully you understand how to treat AND and OR in probability calculations?).

(a) In this part of the question, a number of combinations are acceptable, you could have 5 instances of event A (lets call this 5A for brevity), and 5 instances of event B (5B), or 6 instances of event A (6A) and 4 instances of event B (4B) etc. So, the entire set of scenarios is:

5A and 5B or
6A and 4B or
7A and 3B or
8A and 2B or
9A and 1B or
10A and 0B

I hope that makes sense.