**Question:**

garfield and oldie each toss 3 fair coins. prove that

the probability that oldie gets more head than

garfield is 11/32

garfield and oldie each toss 3 fair coins. prove that

the probability that oldie gets more head than

garfield is 11/32

Heres my working for the qn after considering all the possible cases

P( oldie with 2Heads, 1 tail and garfield with 1head, 2 tails)

p(oldie with 2Heads, 1 tail and garfield with 0 head,3 tails)

p(oldie with 3Heads,0 tail and garfield with 1 head,2 tails)

p(oldie with 3Heads,0 tail and garfield with 2 heads,1 tail)

p(oldie with 3Heads,0 tail and garfield with 0 heads,3tails)

p(oldie with 1Heads,2 tails and garfield with 0 heads,3tails)

These are all the possible cases.

each case correspond to

(1/2)(1/2)(1/2)(1/20(1/2)(1/2)

hence, total probability is ((1/2)to the power of six) X 6 = 8/32

WhaT went wrong?

Thank you!