Q. Suppose that 5 independent trials, each of which results in any of the outcomes 0, 1,
or 2, with respective probabilities 0.3, 0.5, and 0.2, are performed.
Find the probability that both
outcome 1 and outcome 2 occur at least once. (Hint: Consider the complementary probability.)
I dont understand where to start, do i take 5 events for these 5 trails. Is there supposed to be a probability function for this ?
the nCr p^k * (1-p)^n-k thing ? I think that is only for binary probability right ?
Best Answer
Guide:
the complement to "outcome $1$ occurs at least $1$ and Outcome $2$ occurs at least $1$" is "outcome $1$ doesn't occur or outcome $2$ doesn't occur."
Use inclusion-exclusion principle.
Compute $$1 - P(\text{Outcome } 1 \text{ doesn't occur})- P(\text{Outcome } 2 \text{ doesn't occur}) + P(\text{Outcome } 1 \text{ and outcome } 2 \text{ doesn't occur})$$