Question

a bag holds 10 pens: 4 black, 6 blue. if 1 is randomly drawn, then without replacing it, another 1 is drawn, what is the probability of drawing two blue pens? event a: blue pen on 1st draw event b: blue pen on 2nd draw p(a, then b) = ? give your answer as a fraction in simplest form. compound probability dependent events p(a then b) = p(a)·p(b after a)

Explanation:

Step1: Calculate P(A)

$P(A) = \frac{\text{Number of blue pens}}{\text{Total pens}} = \frac{6}{10} = \frac{3}{5}$

Step2: Calculate P(B after A)

After drawing one blue pen, remaining blue pens = 5, total pens = 9. So $P(B \text{ after } A) = \frac{5}{9}$

Step3: Compute P(A then B)

$P(A \text{ then } B) = P(A) \cdot P(B \text{ after } A) = \frac{3}{5} \cdot \frac{5}{9} = \frac{15}{45} = \frac{1}{3}$

Answer:

$\frac{1}{3}$