There are 40 students,
10 have blue eyes, 3 have green and 27 have brown.
In class 12B there are 50 students,
23 have blue eyes, 4 have green and 23 have brown.
One person is chosen at random from
each class to represent the sixth form.
What is the probability that they
both have brown eyes?

answer

≈ 0.31 = 31 %

set up equation

the probability of someone from the first group having brown eyes is

the probability of someone from the second group having brown eyes is

so the probability of both students having brown eyes is*

values

students with brown eyes in first group = 27

total students in first group = 40

students with brown eyes in second group = 23

total students in second group = 50

plug in values and solve

*

=

=

=

≈ 0.31

= 31 %

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

the answer to your question is minor arc.