Certainly! Here's a structured solution with given information, definitions, explanations, and the steps to the probability that the student did NOT an 'B'. --- # Given | Grade | A | B | C | Total | |---------|---|---|---|--------| | Male | 4 | 19 | 14 | | | | 9 | 6 | 15 | 30 | | Total | 23| 25| 29 | 77 | --- # Definitions - **Probability**: The likelihood of an event occurring, given by the ratio of favorable outcomes to total outcomes. \[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] - **Complement of an event**: The event that the original event does not happen. For example, the complement of "getting a B" is "not getting a B". --- # Explanation We are asked to find the probability that a student **did NOT** get a B grade. Using the complement rule: \[ P(\text{not B}) = 1 - P(\text{B}) \] Where: - \( P(\text{B}) \) is the probability that a student got a B grade. --- # Step-by-step Calculation ### Step 1: Find total students who got a B From the table: - Male students with B: 19 - Female students with B: 6 Total students with B: \[ 19 + 6 = 25 \] ### Step 2: Find total number of students Total students: \[ 77 \] ### Step 3: Calculate \( P(\text{B}) \) \[ P(\text{B}) = \frac{25}{77} \] ### Step 4: Calculate \( P(\text{not B}) \) \[ P(\text{not B}) = 1 - P(\text{B}) = 1 - \frac{25}{77} = \frac{77}{77} - \frac{25}{77} = \frac{52}{77} \] --- # **Final Answer** \[ \boxed{ \text{Probability that the student did NOT get a B} = \frac{52}{77} } \] This completes the solution, demonstrating the use of basic probability concepts and the complement rule.