A survey of 150 girls showed that 63 like tea while 87 dislike it. Out of these girls, one girl is chosen at random. What is the probability that the chosen girl
Q (i) likes tea
(ii) dislikes tea

Answer

To solve the problem step by step, we need to calculate the probabilities for both parts of the question.

### Step 1: Understand the total number of girls surveyed
The total number of girls surveyed is given as 150.

### Step 2: Identify the number of girls who like tea
From the survey, we know that 63 girls like tea.

### Step 3: Calculate the probability that a randomly chosen girl likes tea
The probability (P) that a randomly chosen girl likes tea can be calculated using the formula:

\[ P(\text{likes tea}) = \frac{\text{Number of girls who like tea}}{\text{Total number of girls}} \]

Substituting the values we have:

\[ P(\text{likes tea}) = \frac{63}{150} \]

### Step 4: Simplify the fraction
To simplify \(\frac{63}{150}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:

\[ P(\text{likes tea}) = \frac{63 \div 3}{150 \div 3} = \frac{21}{50} \]

### Step 5: Identify the number of girls who dislike tea
From the survey, we know that 87 girls dislike tea.

### Step 6: Calculate the probability that a randomly chosen girl dislikes tea
Using the same probability formula:

\[ P(\text{dislikes tea}) = \frac{\text{Number of girls who dislike tea}}{\text{Total number of girls}} \]

Substituting the values we have:

\[ P(\text{dislikes tea}) = \frac{87}{150} \]

### Step 7: Simplify the fraction
To simplify \(\frac{87}{150}\), we can divide both the numerator and the denominator by their GCD, which is 3:

\[ P(\text{dislikes tea}) = \frac{87 \div 3}{150 \div 3} = \frac{29}{50} \]

### Final Answers
(i) The probability that the chosen girl likes tea is \(\frac{21}{50}\).

(ii) The probability that the chosen girl dislikes tea is \(\frac{29}{50}\).

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