a bet is said to carry 3 to 1 odds if you win 3 for each 1

a bet is said to carry 3 to 1 odds if you win $ 3 for each $ 1 you bet. what must the probability of winning be for this to be a fair bet?

Solution

Amount won = $3

Amount bet = $1

Amount returned = $4

Probability of winning for bet to be fair = Amount bet/amount returned = 0.25

That is, one in 4 bets should win.

Explanation:

If you win one bet after losing 3 bets(that is, one in four bets wins), you gain back the three dollars that you lost in the last 3 bets. Therefore, you break even, and the bet is fair.