For cans of a particular brand of soft drink labelled as containing 330 ml, the actual volume of soft drink in a can varies. Although the company’s quality control assures that the mean volume of soft drink in the cans remains at 330 ml, it is known from experience that the probability of any particular can of the soft drink containing less than 320 ml is 0.0296.
Tilly buys a pack of 24 cans of this soft drink. It may be assumed that those 24 cans represent a random sample. Let L represent the number of cans in the pack that contain less than 320 ml of soft drink.
Find the probability that
(ii)
exactly two of the cans
(iii)
at least two of the cans
contain less than 320 ml of soft drink.