Question

If $E_1, E_2, E_3, E_4$ are mutually exclusive and exhaustive events with respective probabilities $p_1, p_2, p_3$ and $p_4$ , then which of the following is possible?

• A. $p_1 = 0.1, p_2 = 0.2, p_3 = 0.3, p_4 = 0.4$
• B. $p_1 = 0.25, p_2 = 0.35 , p_3 = 0.10, p_4 = 0.05$
• C. $p_1 = 0.4, p_2 = 0.2, p_3 = 0.5, p_4 = 0.3$
• D. $p_1 = 0.6, p_2 = 0.3, p_3 = 0.1, p_4 = 0.1$

Answer 1

Answer: (A)

$p_1 = 0.1, p_2 = 0.2, p_3 = 0.3, p_4 = 0.4$

Answer 2

$p_1 + p_2 + p_3 + p_4$ should be equal to $1$ and none of $p_1, p_2, p_3, p_4$ should be negative.