Question

You place a bet on the number 21 in roulette. The probability of winning is 1 38 , and the company hosting the casino night for a city fundraiser gives the payoff odds as 35:1. What are the odds that the ball will land on the number 21?

1:21


1:38


1:37


1:35

Answer 1

Answer: 1:37

Explanation:

Winning probability/losing probability = 1/38 divided by 37/38; look at the numerators and that your answer which is 1:37

Just in case I got the 37/38 from the knowing there was only one winner from 38 people therefore the rest are losers (37)

Answer 2

The odds that the ball will land on the number 21 is 1:37 .

Hint-

Definition of odds-

Odd is expressed as the ratio of number of favorable events to the number of unfavorable events.

Definition of probability-

Probability is expressed as the ratio of the number of events favorable to a specific event, to the total number of events.

Solution-

If A is the event of landing of ball on 21, then given that

`P(A)=(1)/(38)`

Here, it is the favorable event.

The probability of not landing on 21 is,

`P({A}')=1-P(A)=1-(1)/(38)=(37)/(38)`

Here, it is the unfavorable event.

Now,

Odds that the ball will land on the number 21 =

`\frac{P(A)}{P({A}')}`

`((1)/(38))/((37)/(38)) =(1)/(37) = 1:37`