Explanation
1. Understand the Probability Property:
Since the events A, B, C, and D are mutually exclusive and exhaustive, the sum of their individual probabilities must equal 1.
P(A)+P(B)+P(C)+P(D)=1
2. Set up the Ratio Equation:
Let the given ratio be equal to a constant k:
2P(A)=3P(B)=5P(C)=8P(D)=k
From this, we can express each probability in terms of k:
P(A)=2k
P(B)=3k
P(C)=5k
P(D)=8k
3. Evaluate the Required Expression:
We need to find the value of:
4P(C)+5P(D)2P(A)+3P(B)
Substitute the expressions in terms of k:
Numerator:
2(2k)+3(3k)=4k+9k=13k
Denominator:
4(5k)+5(8k)=20k+40k=60k
4. Final Calculation:
Now, substitute the simplified numerator and denominator back into the fraction:
60k13k
The variable k cancels out:
6013
Correct Option:
(b) 6013
