Even numbers = 2, 4, 6 or 8 = 4/36
Vowels = a, e, i, o, u, y = 6/36
Either-or P = sum of individual Ps
The second problem is unclear. 0 is not an even number. Are the slips being replaced or not? Do you include y as a vowel?
With your conclusions and replacement, you are right.
Consider a bowl containing 36 different slips of paper. Ten of the slips of paper contain one of the set of digits 0 through 9 and 26 slips contain one of the 26 letters of the alphabet. Determine the probability of drawing one slip, what is P (even number or a vowel)
I have 5 even numbers (including 0) and 5 vowels. Would the probability be 5/36+5/36=10/36=5/18?
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