Answer to Question #287607 in Statistics and Probability for Len

Question

during a mathematics festival, students pay 20 pesos for the chance to put icing of a cake on the face of their favorite math teacher.The stidwnt flip a coin twice, if the results are the same both times (two heada or two tails), the students target flips the.same coin three times.If the teacher does not get the same results three times, the students applies icing on the teacher's face.however,ifthe student does not get the same result on his flips, and the teacher gets the same results on his three flips, the teacher applies icing on the student's face.who is more likely to have an icing on his face, the student or the teacher?

Answer 1

Solution:

If any coin tossed, then probability of either head or Tail is $P(H)=P(T)=\frac{1}{2}$

A Student win if two consecutive Toss is either head or Tail:

sample space, $n(S)=\{\{H, H\},\{T, T\},\{H, T\}\{T, H\}\}=4$ ,

winning events, $n(\varepsilon)=4\{4, T\},\{T, T\}\}=2$   

$\therefore$  probability $,P(\varepsilon)=\frac{2}{4}=\frac{1}{2}$

Now, when Teacher flips coin thrice then sample space, 

$n(s) =\{HHH,HHT,HTH,THH, TTT,TTH,THT,HTT\}=8$

 

and for Teacher winning,  $n(E)=\{HHH,TTT\}=2$  

So, Probability of teacher winning $=P(E)=\frac{2}{8}=\frac{1}{4}$  

And Probability of student winning) $=\frac{1}{2}$   

$\therefore$  Student is more likely to have (a win) an icing on Teacher's face.