10 pts In the Monty Hall game, suppose there are 4 doors. A car is behind one door, and a goat is behind one of the three other doors. The game is played the same way. That is, one pick up a door, the host shows you another door with a goat behind it, and asks if you would switch. Figure out the probability you would win a car if you switch vs that if you don't switch. The probability of winner a car by staying with the first pick or switch are 1/4 and 3/8 respectively; always switch 1/4 and 1/2, respectively, hence always switch 1/4 and 1/4; doesn't matter 1/4 and 1/8; always stay Question 20 pts (3 points) This is NOT a multiple choice question. Instead, calculate the binomial probabilities according to the following table first. In a clinical trial of a new drug, the company can involve 100 or 1000 patients. Assume the drug would be 65% effective. 1) Find the largest number k1 such that the binomial probability Pr(Xk2)<0.05 for n=100 and n=1000. 3) calculate the k1/n and k2/n, so that we see the probability of observing the percentage of patients responding to the drug in the range would be about 90% 4) compare and discuss the impact of increasing n=100 to n=1000 in terms what we can say about the true effective rate of the drug. Submit your answer in a file through canvas. k1(pr k2(pr) k1/n k2/n ) n=100 n=1000