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 0.9. 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 information, calculate the probability that Fran will get the gift. Give your answer as a decimal to 2 decimal places.

Probability =

You are a day trader on the stock exchange and you have invested all of your life savings in a portfolio containing 6 stocks. After dwelling on the risks involved in your investment, you have come to the conclusion that if at most half of the stocks in your portfolio are profitable, your investment will be a failure.

Based on empirical data available from the historical records of the stock exchange, you believe that the probability of a stock being profitable is 0.5. Assuming that the profitability of each stock is independent of all the other stocks, calculate the probability (P(F)) that your investment is a failure. Give your answer as a decimal to 2 decimal places.

P(F) =

Ken is a factory worker, who is a part-time 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. Through testing, Ken concludes that if a sample of 100 toys are inspected, the expected number of faulty toys will be 3. Calculate the probability that a randomly chosen toy is faulty. Give your answer as a decimal to 2 decimal places.

Probability that a toy is faulty =