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What is the expected number of coin tosses required before 3 heads in a row show up?

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Try it for 1 head first. Let X be the expected number of flips until you get heads. What are the possible outcomes after 1 flip? There's 1/2 chance of getting heads (H), and there's 1/2 of getting tails (T). We stop when we get H. In other words, you can get H or TH or TTH, etc. Getting T means you've wasted one go, and you still have X flips to go. So, lets define X recursively as X = (1/2)(1) + (1/2)(X+1). This says, "If you've got H the first time, you're done. If you've got T, you've wasted one go and you flip again, hence 1+X." Solving for X, we get X=2. Getting 2 consecutive heads is similar, but you need to add an extra possibility: Getting HT means you've wasted 2 go's and we're still not done. So then we have X = (1/4)(2) + (1/2)(X+1) + (1/4)(X+2). This says, "If you get HH, you're done. If you get T, you've wasted a go and you're not done. If you get HT, you've wasted 2 go's and you're not done." Solving for X gives us X=6. For 3 consecutive heads, it's similar. Think about getting HHT and how this would look mathematically in our equation for X. The expected number of flips is X=14. See if you get the same :)

If you like working with power series, an alternative - but arguably more laborious approach is laid out in 1.42 here www.math.umn.edu/~gennady/hw2.pd

How many shifts will you work!

1 Answer

Strengths and weaknesses

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Why Investec?

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1)Why do you want to work as a receptionist? 2)Why are you interested to work in Hilton group? 3)What you know about this property of Hilton? 4)How do you deal with customer complaints? 5)Where do you see yourself two years from now?

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What do you know about Boss Model Management

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Explain how you would help someone with a problem at Reception?

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How can you improve our business with your responsibilities?

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How would you deal with upset customer?

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