in-gambling-game-a-man-is-paid-5-if-he-gets-all-heads-or-all-tails-when-3-coins-are-tossed-and-he-pays-out-3-if-either-1-or-2-heads-appears-calculate-his-expected-gain-

Question Number 123390 by aurpeyz last updated on 25/Nov/20

i n g a m b l i n g g a m e a m a n i s p a i d $ 5

i f h e g e t s a l l h e a d s o r a l l t a i l s w h e n

3 c o i n s a r e t o s s e d a n d h e p a y s o u t

$ 3 i f e i t h e r 1 o r 2 h e a d s a p p e a r s .

c a l c u l a t e h i s e x p e c t e d g a i n

Answered by talminator2856791 last updated on 25/Nov/20

P ($ 3) = \frac{6}{8} = \frac{3}{4}

P ($ 5) = \frac{2}{8} = \frac{1}{4}

\frac{1}{3} P ($ 3) = P ($ 5)

he gains $ 5 he loses $ 9

expected gain $ - 4