Question

Let's say A keep tossing a fair coin, until he get 2 consecutive heads, define X to be the number of tosses for this process; B keep tossing another fair coin, until he get 3 consecutive heads, define Y to be the number of the tosses for this process. 1) Calculate P{X>Y}

Answer 1

A=Tossing a fair coin, until getting 2 consecutive heads,

Minimum Number of tosses

=(SF)(FS)(FF)(SS)

X =8 tosses

S=Success

F=Failure

B=Tossing a fair coin, until getting 3 consecutive heads.

Minimum Number of tosses

=(SFS)(FSS)(SSF)(SFF)(FSF)(FFS)(FFF)(SSS)

Y =24 Tosses

Probability of an event

`=\frac{\text{Total favorable Outcome}}{\text{Total Possible Outcome}}\\\\P(X)=(SS)/(8)\\\\P(X)=(2)/(8)\\\\P(X)=(1)/(4)\\\\P(Y)=(SSS)/(24)\\\\P(Y)=(3)/(24)\\\\P(Y)=(1)/(8)\\\\(1)/(4)> (1)/(8)\\\\P(X)>P(Y)`