I Fran is about to sit a multiple choice test with 10 questions. She has studied quite hard, and believes that the probability that she will get any particular question correct is 0.85. Fran also believes that the questions are independent, and her performance on each question is independent of her performance on any other question. Fran's parents tell her that if she gets at least 9 of the 10 questions correct, they will buy her a gift. Based on this lnfonnation, calculate the probability that Fran will get the gift. Give your answer as a decimal to 2 decimal places. probability = E I You are a day trader on the stock exchange and you have invested all ofyour life sayings in a portfolio containing 6 stocks. After dwelling on the risks involved in your investment, you have come to the conclusion that if at least half of the stocks in your portfolio are protable, your investment will be a success. Based on empirical data available from the historical records of the stock exchange, you believe that the probability of a stock being protable is 0.45. Assuming that the protability of each stock is independent of all the other stocks, calculate the probability 09(5)) that your investment is a success. Give your answer as a decimal to 2 decimal places. PESJ = :l I Ken is a factory worker, who is a parttime statistics student, and makes toys. He knows that the probability that any given toy on the factory line is faulty is a constant and is independent of whether or not any other toy on the line is faulty. 111is probability is 0.1208 [when rounded to 4 decimal places). Each day, Ken tests the same number of toys. He knows that the expected number of faulty toys each day is 29. Given this infonnation, calculate the number of toys that Ken tests each day. Give your answer as a whole number. Number oftoys Ken tests each day = E