A factory makes 750 cakes every day.
The cakes are orange cakes or lemon cakes.
Each day Aadil takes a sample of 25 cakes to check.
The proportion of the cakes in his sample that are orange is the same as
the proportion of the cakes made that day that are orange.
On Monday Aadil calculated that he needed exactly 7 orange cakes
in his sample.
a) What is the total number of orange cakes that were made on Monday?
orange cakes
On Tuesday, the number of orange cakes Aadil needs in his sample
is 5 correct to the nearest whole number.
Aadil takes at random a cake from the 750 cakes made on Tuesday.
b) What is the lower bound of the probability that the cake
is an orange cake, giving your answer as a decimal?