A die is biased and the probability,

Question

p
, of
throwing a six is known to be less than
1
6
. An
experiment consists of recording the number of
sixes in 25 throws of the die. In a large number
of experiments the standard deviation of the
number of sixes is 1.5. Calculate the value of
p
and hence determine, to two places of decimals,
the probability that exactly three sixes are
recorded during a particular experiment.