Find the probability

[andrewpriest]

Suppose that 10 % of men and 5 % of women have blue eyes. A randomly chosen person has blue eyes. What is the probability that this randomly chosen person is male? You may assume equal proportions for males and females in the population.

 

[Dr.Peterson]

You are asking for P(male | blue eyes). You have been told P(blue eyes | male) and P(blue eyes | female), as well as P(male).

Have you learned about Bayes' Theorem? What you know will determine how this should be answered. (There are other ways.)

(That's why we ask you to show your own thinking, and tell us your context and background.)

 

[pka]

Suppose that 10 % of men and 5 % of women have blue eyes. A randomly chosen person has blue eyes. What is the probability that this randomly chosen person is male? You may assume equal proportions for males and females in the population.

The set of people is partitioned into the sets of males and females. If a person has blue eyes s/he is male or female.
\(\displaystyle \mathscr{P}(B)=\mathscr{P}(B\cap M)+\mathscr{P}(B\cap F)){}\) this from that partition.
Bayes' Theorem tell us that \(\displaystyle \mathscr{P}(B\cap M)=\mathscr{P}(B|M)\cdot\mathscr{P}(M)\), likewise \(\displaystyle \mathscr{P}(B\cap F)=\mathscr{P}(B|F)\cdot\mathscr{P}(F)\)
In the statement of the question you were given all necessary information to complete the answer.
Please do so and post your answers.