Question

A coin is tossed four times. You bet $1 that heads will come up on all four tosses. If this happens, you win $10. Otherwise, you lose your $1 bet.

Find: P(you win) =

P(you lose) =

Average winnings, µ, =

Answer 1

Probability of head in one toss is 0.5

If a coin is tossed 4 times then probability of head on all the 4 tosses is = $(0.5)^4$ = 0.0625

Then probability of you wini is

P(you win) = 0.0625

P(you lose ) = 1 - P(You win)

= 1-0.0625

= 0.9375

You win $10 if you won .

Then average wining =( winning amount) ×P(win)

= 10×0.0625

= $ 0.625

But you have to pay $1 for each game.

So your average gain is = 0.625 - 1 = -0.375

That means loss of $ 0.375