To find the probability of two events without replacement, we can use the general multiplication rule, which states that:
P(A and B) = P(A) * P(B|A)
where P(A and B) is the probability of both events occurring, P(A) is the probability of the first event occurring, and P(B|A) is the probability of the second event occurring given that the first event has occurred.
In this case, we want to find the probability that both members are seniors. Let A be the event that the first member is a senior, and B be the event that the second member is a senior. Then:
P(A) = 12/22
since there are 12 seniors out of 22 members.
P(B|A) = 11/21
since there are 11 seniors left out of 21 members after choosing one senior.
P(A and B) = P(A) * P(B|A)
= (12/22) * (11/21)
= 132/462
= 0.2857
Rounding to two decimal places, the probability is **0.29**.