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Suppose you are eating at cafeteria with two friends.docx

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Nadeem Uddin
Nadeem Uddin

Suppose you are eating at cafeteria with two friends. You have agreed to the following rule to decide who will pay the bill. Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all the three tosses yield the same result the bill will be shared by all. Find the probability that

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Suppose you are eating at cafeteria with two friends. You have agreed to the following rule to decide who will pay the bill. Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all the three tosses yield the same result the bill will be shared by all. Find the probability that (a) Only you have to pay (b) All three will share. Solution = {, , 諮, 諮, 諮, 諮, 諮諮, 諮諮} () = (a) Probability of each person to pay the bill is . Let A be the event that any ones result is different from others. = {, 諮, 諮, 諮, 諮, 諮諮} () =
() = () () = 巨 = () = = . = % There is 25% chance, that only you will pay the bill. (b) Let B be the event that all three will share the bill. If all the three tosses yield the same result the bill will be shared by all. = {, 諮諮} () = () = () () = = . = % There is 25% chance, that bill will be shared by all.

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Suppose you are eating at cafeteria with two friends.docx

  • 1. Suppose you are eating at cafeteria with two friends. You have agreed to the following rule to decide who will pay the bill. Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all the three tosses yield the same result the bill will be shared by all. Find the probability that (a) Only you have to pay (b) All three will share. Solution = {, , 諮, 諮, 諮, 諮, 諮諮, 諮諮} () = (a) Probability of each person to pay the bill is . Let A be the event that any ones result is different from others. = {, 諮, 諮, 諮, 諮, 諮諮} () =
  • 2. () = () () = 巨 = () = = . = % There is 25% chance, that only you will pay the bill. (b) Let B be the event that all three will share the bill. If all the three tosses yield the same result the bill will be shared by all. = {, 諮諮} () = () = () () = = . = % There is 25% chance, that bill will be shared by all.