3. Suppose my friend and I are tossing a biased coin (the chance of the coin lan

Question

3. Suppose my friend and I are tossing a biased coin (the chance of the
coin landing heads is 0.48). I get one dollar each time the coin lands
heads, and I have to pay one dollar to my friend each time it lands
tails. I will stop playing if my net gain is three dollars.

(a)What is the chance that I will stop after exactly three tosses?

(b) What is the chance that I will stop after exactly four tosses?

(c) What is the chance that I will stop after exactly five tosses?

(Hint: Draw a tree like we have in class. At each toss, what are the possible outcomes?)

Explanation / Answer

a)P( I will stop after exactly three tosses)=P(heads on all 3 flips)=(0.48)3 =0.110592

b) P(stop after exactly four tosses)=0 (as net gain 3 can not happen on 4 toss ; for 4 toss if total win is 4 then we do not require 4th flip as condition of net gain 3 is already completed on 3rd flip)

c)

P( chance that I will stop after exactly five tosses)=P(3 heads in first 4 and 4th head on 5th flip)

=P(THHHH)+P(HTHHH)+P(HHTHH)=3*(0.48)4*0.52=0.082811

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