Solving for Unknown Probability in a Binomial Equation
In a binomial experiment with 10 independent trials, the probability of obtaining exactly 4 successes is 0.20. Given that X ~ Binomial(n=10, p), use the binomial probability formula \(P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}\) to set up an equation and solve for the unknown probability of success, \(p\). State your answer to 2 decimal places.
Testing Independence with Incomplete Data
Consider two independent events, A and B. If \(P(A)=0.25\) and the probability that either A or B occurs is \(P(A \cup B)=0.55\), calculate \(P(B)\).