2 integers are selected at random from the integers 1 to 11. The sum of these 2 integers is even. Find the probability that both the selected integers are odd.
Explanation:
There are 11 integers: 6 odd & 5 even.
Sum of two integers is even when either both are even or both are odd.
Both even: Number of ways of selecting two even integers = 5C2 = 10.
Both odd: Number of ways of selecting two odd integers = 6C2 = 15.
∴ Total possible outcomes = 10 + 15 = 25.
∴ Desired outcomes for both integers to be odd = 15.
∴ Required probability = 15/25 = 3/5
Hence, option (b).
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