Elementary Statistics (12th Edition)

a) We know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, hence $probability=\frac{492+306}{492+306+8}=0.99.$ b)Two events are dependent, if the outcome of one effects the outcome of the other. Here the events are independent, because the sampling was done with replacement, also $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, hence $probability=\left (\frac{2518-252}{2518}\right )^{50}=0.00493.$ b) Events are dependent, if the outcome of one effects the outcome of the other. Here the events are dependent, because the choice of the first person effects the opportunities of the second one. $P(A \cap B)=P(A)\cdot P(B|A)$. Hence $P(A \cap B)=\frac{798}{806}\cdot\frac{797}{805}=0.98.$ c)Events are dependent, if the outcome of one effects the outcome of the other. Here the events are independent, because the sampling was done with replacement, also $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, hence $probability=\left (\frac{798}{806}\right )^{25}=0.779.$