Y. A boskel th thed with cards. one for each rette of the aphebet and ove for each dig! \( 0-9 \) One curd hishosen. a) p(number) b) \( P \) (vowel or oven number) c) Plletter after \( N \) or number d) P(letter or odd number)

We are given a box that contains one card for each letter of the alphabet and one card for each digit (0–9). That gives us a total of   26 letters + 10 digits = 36 cards. We then choose one card at random. Let’s solve each part step by step. ────────────────────────────── a) P(number) The “number” cards are the ones labeled with digits (0–9). There are 10 such cards. So,   P(number) = Number of digits⁄Total cards = 10⁄36 = 5⁄18. ────────────────────────────── b) P(vowel or even number) Step 1. Count the vowels among the letters. (Assuming the vowels are A, E, I, O, U, there are 5 vowels.) Step 2. Count the even digits. (The even digits among 0–9 are 0, 2, 4, 6, and 8. That’s 5 even digits.) Since no card is both a letter and a digit (the sets are mutually exclusive), we have total favorable cards = 5 (vowels) + 5 (even numbers) = 10. Thus,   P(vowel or even number) = 10⁄36 = 5⁄18. ────────────────────────────── c) P(letter after N or number) Interpret “letter after N” as the letter that immediately follows N in the alphabet, which is O. There is 1 card for the letter O. Also, “number” cards are the digits, of which there are 10. Again, these two groups do not overlap (O is a letter, not a digit). So, total favorable cards = 1 (O) + 10 (numbers) = 11. Thus,   P(letter after N or number) = 11⁄36. ────────────────────────────── d) P(letter or odd number) Step 1. Count the letters. There are 26 letter cards. Step 2. Count the odd digits. The odd digits among 0–9 are 1, 3, 5, 7, and 9. That’s 5 cards. They are disjoint sets, so total favorable cards = 26 + 5 = 31. Thus,   P(letter or odd number) = 31⁄36. ────────────────────────────── Final Answers: a) 5⁄18 b) 5⁄18 c) 11⁄36 d) 31⁄36