Two dice are thrown and the sum of the numbers which come up is noted. Among the following events: A: sum is even, B: sum is multiple of 3, C: sum is less than 4, D: sum is greater than 11. Which pair of events are mutually exclusive?

Question

The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]

Answer 1

Step 1: Define each event clearly
We list all possible sums for each event: Event A (even sum): \[ \{2,4,6,8,10,12\} \] Event B (multiple of 3): \[ \{3,6,9,12\} \] Event C (sum less than 4): \[ \{2,3\} \] Event D (sum greater than 11): \[ \{12\} \]

Step 2: Check intersections
We check each option: (A and B): \[ \{2,4,6,8,10,12\} \cap \{3,6,9,12\} = \{6,12\} \neq \emptyset \] (B and D): \[ \{3,6,9,12\} \cap \{12\} = \{12\} \neq \emptyset \] (A and C): \[ \{2,4,6,8,10,12\} \cap \{2,3\} = \{2\} \neq \emptyset \] (C and D): \[ \{2,3\} \cap \{12\} = \emptyset \] Thus, only C and D are mutually exclusive.

Economic System	Characteristics
a. Capitalism	i. Private ownership of resources; market-driven economy with minimal government intervention
b. Socialism	ii. Government ownership of key industries; centralized economic planning
c. Mixed Economy	iii. Combination of private and government ownership; focus on social welfare and regulation
d. Market Economy	iv. Private ownership with some government regulation; competition and market forces determine economic outcomes

Two dice are thrown and the sum of the numbers which come up is noted. Among the following events: A: sum is even, B: sum is multiple of 3, C: sum is less than 4, D: sum is greater than 11. Which pair of events are mutually exclusive?

Show Hint

The Correct Option is C

Solution and Explanation

Top Questions on Probability

Questions Asked in Karnataka PGCET exam