So I have a problem here, I know the answer but I have no idea how to solve it. This is one of a sample problem given to us by our prof. Can someone please help me out how to figure this problem out?
Alice and Mary take a math exam. The probability of passing this exam for Alice and Mary is 2/3 and 3/5, respectively. What is the probability that at least one of them will pass the exam?
Best Answer
Fisrt of all we have to assume independence (understood hypothesis)
Let's set the events
"0= not pass"
"1=pass"
And let's analyze all the possible probabilities
$$\mathbb{P}[0;0]=\frac{1}{3}\times \frac{2}{5}=\frac{2}{15}$$
$$\mathbb{P}[0;1]=\frac{1}{3}\times \frac{3}{5}=\frac{3}{15}$$
$$\mathbb{P}[1;0]=\frac{2}{3}\times \frac{2}{5}=\frac{4}{15}$$
$$\mathbb{P}[1;1]=\frac{2}{3}\times \frac{3}{5}=\frac{6}{15}$$
As a verification
$\frac{2}{15}+\frac{3}{15}+\frac{4}{15}+\frac{6}{15}=1$
Now you can answer to any question they ask you, as you know the probability of every elementary event of the event space