A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is:
1. Establish the Probabilities of a Single Throw
Let the probability of getting an even number be and the probability of getting an odd number be .
The problem states that an odd number is thrice (3 times) as likely as an even number:
Since the sum of all probabilities must equal 1:
2. Condition for an Even Sum
When throwing a die twice, the sum of the two numbers is even in exactly two scenarios:
Case 1: Both numbers are odd
Case 2: Both numbers are even
3. Calculate the Probability for Each Case
Probability of (Odd, Odd):
Probability of (Even, Even):
4. Total Probability for an Even Sum
The total probability is the sum of these two mutually exclusive cases:
5. Simplifying the Result
Divide the numerator and denominator by 2 to match the format of the options:
Correct Option: (b)
If a number is selected at random from natural numbers 1,2,……,100,then …
