mr. armstrong has to select two students from a class of 23 girls and 25 boys. what is the probability that…
mr. armstrong has to select two students from a class of 23 girls and 25 boys. what is the probability that both students chosen are boys?
Answer
Explanation:
Step1: Calculate the total number of students
$$23 + 25 = 48$$
Step2: Determine probability of first student being a boy
$$P(B_{1}) = \frac{25}{48}$$
Step3: Determine probability of second student being a boy
$$P(B_{2} | B_{1}) = \frac{24}{47}$$
Step4: Multiply the probabilities for both events
$$P(B_{1} \cap B_{2}) = \frac{25}{48} \times \frac{24}{47}$$
Step5: Simplify the resulting fraction
$$\frac{25 \times 1}{2 \times 47} = \frac{25}{94}$$
Answer:
$\frac{25}{94}$ (or approximately 0.266)