Question

Calculating expected number of throws to get 5 consectuive heads

Answer 1

Answer:

62

Step-by-step explanation:

Let e be the expected number of tosses. It is clear that e is finite.

Start tossing. If we get a tail immediately (probability 1/2) then the expected number is e+1. If we get a head then a tail (probability 1/4), then the expected number is e+2.

Continue …. If we get 4 heads then a tail, the expected number is e+5. Finally, if our first 5 tosses are heads, then the expected number is 5. Thus

e= 1/2(e+1)+ 1/4(e+2)+ 1/8(e+3)+ 1/16(e+4)+ 1/32(e+5)+ 1/32(5).

Solve this linear equation for e -

We get e = 62.

Hope it helps..

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