Question

1. a bag contains 3 blue stones, 5 red stones and 2 white stones. what is the probability of picking a blue stone, keeping it, and then picking a white stone? (1 pt)

Explanation:

Step1: Find total number of stones

Total stones = 3 (blue) + 5 (red) + 2 (white) = 10.

Step2: Probability of picking blue first

Probability of blue, \( P(B) = \frac{3}{10} \).

Step3: Update total after removing blue

After picking blue, total stones = 10 - 1 = 9.

Step4: Probability of picking white next

Probability of white, \( P(W) = \frac{2}{9} \).

Step5: Multiply probabilities (dependent events)

Combined probability = \( P(B) \times P(W) = \frac{3}{10} \times \frac{2}{9} \).
Simplify: \( \frac{3 \times 2}{10 \times 9} = \frac{6}{90} = \frac{1}{15} \).

Answer:

\(\frac{1}{15}\)