If $A$ and $B$ are two mutually exclusive events such that $P(... | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

MathematicsProbability

If $A$ and $B$ are two mutually exclusive events such that $P(A) = 0.3$ and $P(B) = 0.4$ , find the probability that neither $A$ nor $B$ occurs.

0.7

0.3

0.1

0.6

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsProbability

Option B

0.3

Quick Summary:

For mutually exclusive events, simply subtract the sum of individual probabilities from 1. Result is 1 - (0.3 + 0.4) = 0.3.

📐MAMath SolutionDirect Formula

📋 Given

Probability of event A, P(A) = 0.3. Probability of event B, P(B) = 0.4. Events A and B are mutually exclusive.

🔢 Formula Used

P(neither A nor B)=1−P(A∪B)=1−(P(A)+P(B))P(\text{neither } A \text{ nor } B) = 1 - P(A \cup B) = 1 - (P(A) + P(B))P(neither A nor B)=1−P(A∪B)=1−(P(A)+P(B))

⚡ Exam Hall Shortcut / Speed Trick

For mutually exclusive events, simply subtract the sum of individual probabilities from 1. Result is 1 - (0.3 + 0.4) = 0.3.

⚠️ Common Student Trap / Pitfall

Students often mistakenly assume $P(A \cup B) = P(A) \times P(B)$ instead of using the additive law, or they forget to subtract the sum from 1 to find the complement.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define Additive Law

Since events A and B are mutually exclusive, their intersection $P(A \cap B) = 0$ . The probability of their union is the sum of their individual probabilities.

P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B)P(A∪B)=P(A)+P(B)

Calculate Union

Substitute the given values into the additive formula: $P(A \cup B) = 0.3 + 0.4 = 0.7$ .

P(A∪B)=0.7P(A \cup B) = 0.7P(A∪B)=0.7

Find Probability of Neither

The probability of neither A nor B occurring is the complement of the union of A and B, calculated as $1 - P(A \cup B)$ .

P(neither A nor B)=1−0.7=0.3P(\text{neither } A \text{ nor } B) = 1 - 0.7 = 0.3P(neither A nor B)=1−0.7=0.3

✅

B is correct because the probability of neither A nor B is $1 - (0.3 + 0.4) = 0.3$ .

Core Concepts Used

Click any tag to open in AI Tutor

Mutually Exclusive Events Complement Rule Additive Law of Probability

💡 EXAM TIP

This concept of complements is foundational for 'at least one' problems in combinatorics and Bayesian probability calculations.

Was this solution helpful?

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)