Unfortunately, I couldn't solve this question. Actually, I am very suspicious about whether the question is correct or not.
An experiment has a sample space that consists of 8 equally likely outcomes. $ S = \{x_1, x_2, …, x_8\} $. Three events are defined as $ A = \{x_2, x_4, x_6, x_8\}, B = \{x_1, x_3, x_6, x_7\}, C = \{x_1, x_2, x_3, x_5\} $ . Find the probabilities of the following events.
a)$ A \cap B$
b) $ \overline{A \setminus B}$
c)$ A \cap (B\cup\overline{A})$
d $\overline{A \cap B \cap C} $
I thought for question in a $ A \cap B = \{x_6\} $ so $ P(A \cap B) = 1/8 $ but i am not sure
Best Answer
Question seems correct. If you intersect events $A$ and $B$ you get the event $\{x_6\}$. The probability of event $\{x_6\}$ happening is just $\frac{1}{8}$, because there are 8 outcomes en all are equally likely (thus every outcome has probability $\frac{1}{8}$). The event $\{x_6\}$ consists of only 1 outcome, namely the outcome $x_6$ so the probability is just $\frac{1}{8}$.
Hint for following exercises: probability of an event consisting of 2 outcomes is $\frac{2}{8}$, probability of an event consisting of 3 outcomes is $\frac{3}{8}$, the probability of an event consisting of 4 outcomes is $\frac{4}{8}$, ... . You thus need to do the set operations first and see how much outcomes are still left. Count these outcomes and this will give you the probability.