A game wheel has 38 slots numbered 1-38, respectively. Matt places a bet on the odd numbers and Julie places a bet on numbers 10, 11, 13, and 14. What is the probability of landing on an odd number or 10, 11, 13, or 14? Show all work.

1. 2/3

2. 19//38

3. 9/19

4. 21/38

Odd numbers are of the from a (n) = a+d (n-1) where a=1 and d=2 so

a (n) = 1+2 (n-1) = 2n-1 and we need the number of odds in the range 1 to 38

2n-1≤38

2n≤39

n≤19.5, so there are 19 odd numbers in [1,38]

And since Julie bet on two even numbers as well, the probability of getting an odd number or the two evens she picked is:

(19+2) / 38

21/38