[Math] the probability that a person has both of these attributes

probability

The probability that a blue-eyed person is left-handed is $\frac{1}{7}$.

The probability that a left-handed person is blue-eyed is $\frac{1}{3}$ .

The probability that a person has neither of the attributes is $\frac{4}{5}$.

What is the probability that a person has both attributes?

I just don't know how they got the answer

Answer: $\frac{1}{45}$

Best Answer

Hint:

$P\left[L\mid B\right]=\frac{1}{7}$ i.e. $P\left[L\cap B\right]=\frac{1}{7}P\left[B\right]$

$P\left[B\mid L\right]=\frac{1}{3}$ i.e. $P\left[L\cap B\right]=\frac{1}{3}P\left[L\right]$

$1-P\left[L\cup B\right]=\frac{4}{5}$

These equations are enough to find $P\left[L\cap B\right]$

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