Question

If the odds on a bet are 36:1 against, what is the probability of winning? Express your answer as a fraction.

Answer 1

The odds on a bet are 36:1 against.

These odds indicate that if you play 37 times, you are expected to lose 36 times and win 1 time.

Let A:B represent the odds

The probability of the first value, A, can be calculated as:

`P(A)=(A)/((A+B))`

And the probability of the second value, B, can be calculated as:

`P(B)=(B)/((A+B))`

Using this, you can calculate the probability of winning:

The odds are against, which indicates that the ratio given is lose-win, so the probability of winning can be calculated as follows:

`\begin{gathered} P(win)=(win)/((lose+win)) \\ P(win)=(1)/(36+1) \\ P(win)=(1)/(37) \end{gathered}`

The probability of winning the bet is 1/37.