Answer-
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
[tex]P(A)=\frac{1}{38}[/tex]
Here, it is the favorable event.
The probability of not landing on 21 is,
[tex]P({A}')=1-P(A)=1-\frac{1}{38}=\frac{37}{38}[/tex]
Here, it is the unfavorable event.
Now,
Odds that the ball will land on the number 21 =
[tex]\frac{P(A)}{P({A}')}[/tex]
[tex]\frac{\frac{1}{38}}{\frac{37}{38}} =\frac{1}{37} = 1:37[/tex]
