Fundamental counting principle, permutations, and combinations:

Lesson 5: Solving Probability Problems That Involve Permutations and Combinations Focus The pigpen cipher is a geometric substitution cipher in which symbols are substituted for letters. The symbols are derived from fragments of two tic-tac-toe boards and two X's as shown. B Using the pigpen cipher, the phrase "x marks the spot" would look like the following: > aJov >no X MARKS THE SPO T How could you determine the probability of someone guessing a coded message? Suppose you had some understanding of how the cipher worked. How would that change the probability of guessing correctly? Is order important when decoding a message? Calculating the probabilities of more complex questions can often be assisted by permutations and combinations. Both can be used to help determine the number of favourable outcomes and the number of total outcomes.Use the following information to answer the next 2 questions. Suppose you wrote the following message using the pigpen cipher from Lesson 3. =] 121 ] Question 2 (2 points) Algebraically determine 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) Algebraically determine the probability of the person correctly guessing the following message on the first try if the person knew that was an 's. (2 marks) I i T i Hint: You can assume that if you guess any repeated symbol in the sequence correctly for the first time, you will also guess the same symbol again correctly