Thanks Question 3 224412 marks a 16 people in a pub are each

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Question 3 [(2+2+4+4-12) marks] (a) 16 people in a pub are each given a fair coin and asked to stand up and flip the coin. If the tossed coin comes up \'heads\', they are told to toss the coin again, while those people who flipped a coin that came up tails\' have to sit down. If they do this for four rounds in total, how many people would you expect to remain standing after the fourth round? (b) If you were to play the pub game as described above, but wanted it to last 6 rounds before the same number of people as in part (a) were left standing, how many people would need to play from the beginning? Page 1 of 2

Solution

(a)

While flipping a coin

chance of head (H)= 1/2

Chance of tail (T) = 1/2

In first round

There is 16 people who flip the coin.

Number of Heads = 1/2 * 16 = 8

Number of tails = 1/2 * 16 = 8

So, the people who gets tail have to sit down.

Now, 8 people remains and flip the coin in second round.

Likewise, 4 have to si down and 4 flip the coin in third round.

Now, 2 have to sit down and 2 flip the coin in forth round .

Then, in forth round ,

1 have to sit down

and 1 remains standing who get head after forth round.

(b)

To remain 1 people standing after six rounds

there shound be 2 people in 6th round

4 people in 5th round.

8 people in 4th round.

16 people in 3rd round

32 people in 2nd round

64 people in 1st round.

So there is total 64 people need to play from starting.