If you're not too comfortable yet with these probability problems, each time you work one you might want to back up and think about what the exact model for the problem is. In this case: Experiment: Pick one letter from the alphabet at random. Sample space: There are 26 possible outcomes. $S = \{a, b, c, \ldots, z\}$. Probability distribution: The problem is implicitly assuming all choices are equally likely here, so we have $P(\{\text{letter}\}) = 1/26$ for every letter. Event: The letter you've chosen is contained in the word "house" or "phone." So $E = \{x \in S \mid x \text{ is one of } h, o, u, s, e, p, n \}$. That is, $E$ is just the set $\{h, o, u, s, e, p, n\}$. (You can break this down into a union of two separate events, as other answers are suggesting, also.) The problem wants to know $P(E)$, which equals $P(\{h\}) + P(\{o\}) + \cdots + P(\{n\})$. A) A letter is drawn at random from those in the word “ENGLISH”, what is the probability that: 1. it is a vowel or consonant? 2. E or H? B) If a card is drawn from a deck, what is the probability that: 3. it is a spade or heart? 4. A king or a queen?
Answer: 1, 42 for vowels and 2520 for consonant 2, 7 for both E and H Step-by-step explanation: |