Question

A biased coin has probability 0.6 of turning up heads. You win $x if a head comes up and you lose $y if a tail comes up. If your expected winnings is $0, what is the relationship between x and y?

Answer 1

Answer:

x,y will be in the ratio 2:3

Step-by-step explanation:

Given that a biased coin  has probability 0.6 of turning up heads

In other words, number of heads we obtain by tossing the coin would be binomial with p = 0.6 and q =1-p =0.4

If you toss one time, the distribution of U, no of heads would be

U    0     1

p   0.4   0.6

Winning amount would be 0.6x and losing amount would be 0.4y

If these two are equal then we have

$0.6x=0.4y\\Or x:y = 2:3$