Question

a jar holds 15 beads: 10 purple, 5 orange. if 1 is randomly drawn, then without replacing it, another 1 is drawn, what is the probability both beads are purple? event a: purple bead on 1st draw event b: purple bead 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)

Total beads = 15, purple beads = 10. So $P(A) = \frac{10}{15} = \frac{2}{3}$.

Step2: Calculate P(B after A)

After drawing 1 purple bead, remaining beads = 14, remaining purple beads = 9. So $P(B \text{ after } A) = \frac{9}{14}$.

Step3: Compute P(A then B)

Multiply the two probabilities: $P(A) \cdot P(B \text{ after } A) = \frac{2}{3} \cdot \frac{9}{14} = \frac{18}{42} = \frac{3}{7}$.

Answer:

$\frac{3}{7}$