Explanation
Solution
Step 1: Determine the probabilities of Odd and Even
Let the probability of getting an even number be P(E)=x.
According to the problem, the probability of getting an odd number is P(O)=3x.
Since an outcome must be either even or odd:
So:
Step 2: Identify when the sum is even
For the sum of two numbers to be even, there are two possible cases:
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Both numbers are Odd: (O,O)
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Both numbers are Even: (E,E)
Step 3: Calculate the probability for each case
Since the two throws are independent events:
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Case 1: Both are Odd
P(O,O)=P(O)×P(O)=43×43=169
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Case 2: Both are Even
P(E,E)=P(E)×P(E)=41×41=161
Step 4: Find the total probability
Total Probability P(Sum is Even)=P(O,O)+P(E,E)
Simplifying the fraction:
Correct Option: 2. 5/8
