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A school has five houses A, B,C,D and E....

A school has five houses `A`, `B`,`C`,`D` and `E`. A class has `23` students, `4` from houses `A`, `8` from house `B` and `5` from house `C`, `2` from house `D` and rest from house `E`. A single student is selected at random to be the class monitor. The probability that the selected student is not from `A`, `B` and `C` is

A

`(4)/(23)`

B

`(6)/(23)`

C

`(8)/(23)`

D

`(17)/(23)`

Text Solution

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The correct Answer is:
To solve the problem, we need to find the probability that a randomly selected student is not from houses A, B, and C. Let's break down the solution step by step. ### Step 1: Determine the total number of students The total number of students in the class is given as 23. ### Step 2: Identify the number of students from each house - Students from house A = 4 - Students from house B = 8 - Students from house C = 5 - Students from house D = 2 - Students from house E = (Total students - Students from A, B, C, D) First, we calculate the number of students from houses A, B, and C: \[ \text{Total from A, B, C} = 4 + 8 + 5 = 17 \] ### Step 3: Calculate the number of students from house E Now, we can find the number of students from house E: \[ \text{Students from E} = \text{Total students} - \text{Total from A, B, C} - \text{Students from D} \] \[ \text{Students from E} = 23 - 17 - 2 = 4 \] ### Step 4: Determine the number of students not from A, B, and C To find the number of students not from houses A, B, and C, we can add the students from houses D and E: \[ \text{Students not from A, B, C} = \text{Students from D} + \text{Students from E} \] \[ \text{Students not from A, B, C} = 2 + 4 = 6 \] ### Step 5: Calculate the probability The probability \( P \) that a randomly selected student is not from houses A, B, and C is given by the formula: \[ P(\text{not from A, B, C}) = \frac{\text{Number of students not from A, B, C}}{\text{Total number of students}} \] \[ P(\text{not from A, B, C}) = \frac{6}{23} \] ### Final Answer Thus, the probability that the selected student is not from houses A, B, and C is: \[ \frac{6}{23} \] ---
To solve the problem, we need to find the probability that a randomly selected student is not from houses A, B, and C. Let's break down the solution step by step. ### Step 1: Determine the total number of students The total number of students in the class is given as 23. ### Step 2: Identify the number of students from each house - Students from house A = 4 - Students from house B = 8 ...
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