Question

1) IF THE PROBABILITY THAT A FOOTBALL TEAM WILL WIN THEIR NEXT GAME IS 80%, WHAT ARE THE ODDS IN FAVOR OF THEM WINNING?2) IF THE ODDS AGAINST A PARTICULAR CANDIDATE WINNING AN ELECTION ARE 9 TO 5, WHAT IS THE PROBABILITY THAT THE CANDIDATE WILL WIN?

Answer 1

1) Given the probability of an event to occur, the odds will be the quotient of the probability of that event to occur and the probability of that event not to.

It means that the odds can be calculated this way:

`O=(P)/(1-P)`

The probability for the football team to win is 80% or, in other terms, 0.8. The odds will be:

`\begin{gathered} O=(0.8)/(1-0.8) \\ O=(0.8)/(0.2) \\ O=4 \end{gathered}`

It means that the odds in favor for them to winning are 4 to 1.

2) Use the formula given above to find the probability of the candidate to win:

`\begin{gathered} (9)/(5)=(P)/(1-P) \\ (9)/(5)(1-P)=P \\ (9)/(5)-(9)/(5)P=P \\ (9)/(5)=P+(9)/(5)P \\ (9)/(5)=(14)/(5)P \\ P=(9)/(5)\cdot(5)/(14) \\ P=(9)/(14) \end{gathered}`

It means that the probability of the candidate to win is 9/14.