a. Since the events in the sample space are equally likely, the probability of each event is 1/6.
Therefore, P(N) = 1/6.
b. The complement of event L, denoted by Lc, is the event that L does not occur.
Since each event in the sample space is equally likely, the probability of an event not occurring is the complement of the probability of the event occurring.
Therefore, P(Lc) = 1 - P(L) = 1 - 1/6 = 5/6.
c. The union of events K, M, and O (denoted as K U M U O) is the event that at least one of these three events occurs.
To find the probability of this union, we can sum the probabilities of each individual event and subtract the overlapping probabilities.
P(K U M U O) = P(K) + P(M) + P(O) - P(K ∩ M) - P(K ∩ O) - P(M ∩ O) + P(K ∩ M ∩ O).
Since each event is equally likely, this simplifies to:
P(K U M U O) = 1/6 + 1/6 + 1/6 - 0 - 0 - 0 + 0 = 3/6 = 1/2.
Therefore, P(K U M U O) = 1/2.
A sample space S yields six equally likely events, K, L, M, N, O, and P.
a. Find P(N). (Round your answer to 2 decimal places.)
b. Find P(Lc). (Round your answer to 2 decimal places.)
c. Find P(K U M U O). (Do not round intermediate calculations. Round your answer to 2 decimal places.)
1 answer