S2 clarification on how to work out probability question - pints of milk combinations

You are given that the probability of a pint of milk containing less than 1 pint = 0.005. A crate contains 24 bottles.

First part of question I can do ok.

Find the probability that no bottles contain less than 1 pint of milk.

Probability that a bottle does NOT contain less than 1 pint = 1 - 0.005 = 0.995.

prob no bottles in crate contain less than 1 pint = 0.995^24 = 0.8865. This answer agrees with my answer sheet.

But I want to check I am doing the second part of the question correctly as it is trickier.

Find the probability that at most 1 bottle contains less than 1 pint of milk.

Well this probability must be higher than ALL 24 NOT less than 1 pint because one of them can or can not.

So is it worked out like this:

0.995^23 * 1

1 - meaning includes both options - ie could be less than 1 pint but doesn't have to be?

0.995^23 = 0.8911

but book answer says 0.9936 - so mine must be wrong?

How do I do this?

[Just].

Reply 1

SherlockHolmes

The probability of a bottle containing less than 1 pint of milk is distributed binomially.

Original post by acomber

Find the probability that at most 1 bottle contains less than 1 pint of milk.

This is the equal to the probability no bottles contain less than 1 pint of milk + the probability of 1 bottle containing less than 1 pint of milk.

Remember that there are 24C1 ways for 1 of the 24 bottles to contain less than 1 pint of milk.

(edited 9 years ago)

Reply 2

acomber

Original post by SherlockHolmes

The probability of a bottle containing less than 1 pint of milk is distributed binomially.

This is the equal to the probability no bottles contain less than 1 pint of milk + the probability of 1 bottle containing less than 1 pint of milk.

Remember that there are 24C1 ways for 1 of the 24 bottles to contain less than 1 pint of milk.