Question 1191525: MAT 145: Topics In Contemporary Math
Probability
1) Suppose we perform an experiment where we pick a two letters: one from the word
“COBRA” and one from the word “FISH”. What is the sample space of all possible
outcomes?
Suppose V is the event that we select exactly one vowel. What are the outcomes in this event?
Suppose B is the event we select the B from the word COBRA. What are the outcomes in this event?
What are the outcomes in 𝑉 𝑎𝑛𝑑 𝐵?
What are the outcomes in 𝑉 𝑜𝑟 𝐵?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to break down this probability problem:
**1. Sample Space:**
The sample space consists of all possible pairs of letters, one from each word. We can represent them as (letter from COBRA, letter from FISH):
S = {(C, F), (C, I), (C, S), (C, H), (O, F), (O, I), (O, S), (O, H), (B, F), (B, I), (B, S), (B, H), (R, F), (R, I), (R, S), (R, H), (A, F), (A, I), (A, S), (A, H)}
There are 5 letters in "COBRA" and 4 letters in "FISH", so the sample space has 5 * 4 = 20 possible outcomes.
**2. Event V (Exactly One Vowel):**
V = {(C, I), (O, F), (O, I), (O, S), (O, H), (B, I), (R, I), (A, F), (A, I), (A, S), (A, H)}
The vowels in "COBRA" are O and A, and the vowel in "FISH" is I. Event V includes all pairs where one letter is a vowel and the other is a consonant.
**3. Event B (Selecting B from COBRA):**
B = {(B, F), (B, I), (B, S), (B, H)}
This event includes all pairs where the first letter is B.
**4. Event V and B (Exactly One Vowel AND Selecting B):**
V ∩ B = {(B, I)}
This event includes only the outcome where we select B from "COBRA" and I from "FISH".
**5. Event V or B (Exactly One Vowel OR Selecting B):**
V ∪ B = {(C, I), (O, F), (O, I), (O, S), (O, H), (B, F), (B, I), (B, S), (B, H), (R, I), (A, F), (A, I), (A, S), (A, H)}
This event includes all outcomes that are in V, or in B, or in both. We simply combine the outcomes from the two events, without repeating any outcomes.
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