Explanation
Step 1: Calculate probabilities for Bag 1
Total ways to draw 2 marbles out of 8 from Bag 1:
n(S1)=(28)=2×18×7=28
Probability of getting 2 Red marbles (2R):
P(2R1)=28(25)=2810
Probability of getting 2 White marbles (2W):
P(2W1)=28(23)=283
Probability of getting 1 Red and 1 White marble (1R,1W):
P(1R1,1W1)=28(15)×(13)=285×3=2815
Step 2: Calculate probabilities for Bag 2
Total ways to draw 2 marbles out of 8 from Bag 2:
n(S2)=(28)=2×18×7=28
Probability of getting 2 Red marbles (2R):
P(2R2)=28(22)=281
Probability of getting 2 White marbles (2W):
P(2W2)=28(26)=2815
Probability of getting 1 Red and 1 White marble (1R,1W):
P(1R2,1W2)=28(12)×(16)=282×6=2812
Step 3: Combine the cases to find Total Probability
Since drawing from Bag 1 and Bag 2 are independent events, we multiply the individual probabilities for each case and then add the results of the three cases together:
Total Probability (P)=[P(2R1)×P(2R2)]+[P(2W1)×P(2W2)]+[P(1R1,1W1)×P(1R2,1W2)]
P=(2810×281)+(283×2815)+(2815×2812)
P=28×2810+45+180
P=784235
Let's simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 5 or check other factors. Here, 784 is not divisible by 5. Let's look closely at the step value: 784235 does not match options (a), (b), or (c).
Therefore, the correct choice is (d) none.
