A page of text is analysed, and of the 150 words on it, 30 are nouns, 10 of which start with a vowel. Of the words that are not nouns, 85 of them do not start with vowels.
a. If the word on the page is chosen at random, what is the probability that it is a noun?
b. How many words on the page start with vowels.
Can you please tell me if i would also use a venn diagram or a two way table thanks
a. 30/150 = ?
b. 10 + (120-85) = ?
To answer these questions, you can use a two-way table. The table will help us organize the information and calculate the probabilities.
Step 1: Create a two-way table.
Nouns Not Nouns Total
Starts with vowel 10 ? ?
Doesn't start with vowel ? 85 ?
Total 30 120 150
Step 2: Fill in the given information.
- We know there are 30 nouns in total.
- Out of the 30 nouns, 10 start with a vowel.
- We know there are 85 words that are not nouns.
- Out of the words that are not nouns, 85 do not start with vowels.
Nouns Not Nouns Total
Starts with vowel 10 ? ?
Doesn't start with vowel ? 85 ?
Total 30 120 150
Step 3: Calculate the missing values.
- To find the total number of words that start with a vowel, we can subtract the number of nouns that start with a vowel (10) from the total number of nouns (30). So, the number of words that start with a vowel is 30 - 10 = 20.
Nouns Not Nouns Total
Starts with vowel 10 ? 20
Doesn't start with vowel ? 85 ?
Total 30 120 150
- To find the number of words that are not nouns and don't start with vowels, we subtract the number of words that are not nouns and start with vowels (which is given as 85) from the total number of words that are not nouns. So, the number of words that are not nouns and don't start with vowels is 85 - 10 = 75.
Nouns Not Nouns Total
Starts with vowel 10 ? 20
Doesn't start with vowel ? 85 75
Total 30 120 150
Step 4: Calculate the probabilities.
a. Probability that a randomly chosen word is a noun:
P(noun) = Number of nouns / Total number of words = 30 / 150 = 1/5 = 0.2
b. Number of words on the page that start with vowels: 20
In this case, using a two-way table helps organize the information and calculate the probabilities more easily.
To solve this problem, we can use a two-way table to organize the information. This will help us visualize the relationship between nouns and non-nouns, as well as the starting vowels and non-starting vowels.
First, let's create the two-way table:
| Nouns | Non-Nouns
------------|----------|-----------
Starts with | |
a vowel | |
------------|----------|-----------
Does not | |
start with | |
a vowel | |
Now, let's fill in the given information:
| Nouns | Non-Nouns
------------|---------|-----------
Starts with | 10 | ?
a vowel | |
------------|---------|-----------
Does not | ? | 85
start with | |
a vowel | |
From the given information, we know that there are 30 nouns and 85 non-nouns that do not start with vowels. We are also given that 10 of the nouns start with a vowel.
To calculate the missing values, we can use the fact that there are a total of 150 words on the page:
Total words on the page = Nouns + Non-Nouns
150 = Nouns + Non-Nouns
Since we know that there are 30 nouns, we can substitute the value:
150 = 30 + Non-Nouns
Non-Nouns = 150 - 30
Non-Nouns = 120
Now we can fill in the remaining values in the table:
| Nouns | Non-Nouns
------------|---------|-----------
Starts with | 10 | ?
a vowel | |
------------|---------|-----------
Does not | 20 | 85
start with | |
a vowel | |
From the completed two-way table, we can answer the questions:
a. The probability that a word chosen at random is a noun is given by the ratio of the number of nouns to the total number of words:
Probability = Number of Nouns / Total words
Probability = 30 / 150
Probability = 1/5
Therefore, the probability that a word chosen at random is a noun is 1/5.
b. To find the number of words on the page that start with vowels, we need to add the two values in the "Starts with a vowel" row:
Number of words that start with vowels = Nouns (starts with a vowel) + Non-Nouns (starts with a vowel)
Number of words that start with vowels = 10 + 20
Number of words that start with vowels = 30
Therefore, there are 30 words on the page that start with vowels.
In conclusion, we used a two-way table to organize the given information and solve the problem.