Question

1. a standard number cube is tossed. find p(even or prime).

options: (\frac{2}{3}), (\frac{5}{6}), (\frac{1}{6}), (\frac{1}{2})

Explanation:

Step1: Define sample space

Sample space: $S = \{1,2,3,4,5,6\}$, $n(S)=6$

Step2: Identify even numbers

Even numbers: $E = \{2,4,6\}$, $n(E)=3$

Step3: Identify prime numbers

Prime numbers: $Pr = \{2,3,5\}$, $n(Pr)=3$

Step4: Find intersection of sets

$E \cap Pr = \{2\}$, $n(E \cap Pr)=1$

Step5: Apply addition rule

$$P(E \text{ or } Pr) = P(E) + P(Pr) - P(E \cap Pr)$$
$$=\frac{3}{6}+\frac{3}{6}-\frac{1}{6}=\frac{5}{6}$$

Answer:

B. $\frac{5}{6}$