Suppose that A1, A2,, An are completely independent events of a sample space with P(Ai) = pi, with pi (i) Verify that the probability

Suppose that A1, A2,…, An are completely independent events of a sample space Ω

with P(Ai) = pi, with pi

(i) Verify that the probability that exactly one of the events A1, A2,…, An appear equals

(ii) If we throw two dice n times, what is the probability that a double four appears exactly once? What can we say about this probability as n grows larger (n → ∞)?

n Pi (1-P)(1-P2)(1-Pn)1-Pi i=1