Question

In a class, there are 80% of the students who like English and 30% of the students who likes English and Mathematics, and then what is the percentage of students those who like Math, also like English? Solve it using Conditional probability.

Answer 1

To find the percentage of students who like Mathematics given that they like English, we can use conditional probability. The conditional probability of event \( A \) given event \( B \) (\( P(A|B) \)) is calculated using the formula:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

In this case:

• A is the event of liking Mathematics.
• B is the event of liking English.
• \( P(\text{Likes English}) = 0.8 \) (80% of students like English).
• \( P(\text{Likes English and Mathematics}) = 0.3 \) (30% of students like both English and Mathematics).

 

Now, we can calculate \( P(\text{Likes Mathematics | Likes English}) \):

\[ P(\text{Likes Mathematics | Likes English}) = \frac{P(\text{Likes English and Mathematics})}{P(\text{Likes English})} \]

\[ P(\text{Likes Mathematics | Likes English}) = \frac{0.3}{0.8} \]

\[ P(\text{Likes Mathematics | Likes English}) = 0.375 \]

So, the percentage of students who like Mathematics given that they like English is \( 37.5\% \).

Answer 2

Given:

• 80% of the students like English
• 30% of the students like both English and Mathematics

We want to find:

• The percentage of students who like Math, also like English

Solution:

We can use the formula for conditional probability to solve this problem:

P(A|B) = P(A and B) / P(B)

 

where:

 

• P(A|B) is the probability of event A happening given that event B has already happened
• P(A and B) is the probability of both events A and B happening
• P(B) is the probability of event B happening

 

In this case, we want to find P(Math|English), which is the probability of a student liking Math given that they like English. We know that P(English) = 0.8 and P(English and Math) = 0.3. Plugging these values into the formula, we get:

 

P(Math|English) = 0.3 / 0.8 = 0.375

 

Converting this to a percentage, we get:

 

P(Math|English) = 0.375 * 100% = 37.5%

 

Therefore, 37.5% of the students who like English also like Math.