7. a. Suppose you wrote the following message using the pigpen cipher from the lessons. 3J> i. What is the probability that an interceptor would correctly guess the message on the first try if the interceptor assumed each symbol corresponded to a letter of the alphabet? 2 marks ii. What is the probability of the person correctly guessing the following message on the first try if that person knew vwas an s? 3 marks :Tvvrvvrjj (Hint: You can assume that if you guess the first [ correctly, you will also guess the [ correctly.) b. A person has bought one ticket each for two separate lotteries. Determine the probability of winning a grand prize for the two lotteries. i. For the first lottery, 5 random numbers are drawn from 40. To win the grand prize, you need to select the correct 5 numbers. 2 marks ii. For the second lottery, 4 random numbers are drawn one at a time from 35. To win the grand prize, you need to select the correct 4 numbers in the correct order. 2 marks iii. A person is more likely to win the first lottery described in question 1.a., even though the first lottery requires a person to have more correct numbers (5 compared to 4) selected from a larger set of numbers (40 compared to 35). Explain why this is true. 1 mark