Question

we have a deck of 10 cards numbered from 1 to 10. some are grey and some are white, as shown below. the cards numbered 1, 5, 9, and 10 are grey. the cards numbered 2, 3, 4, 6, 7, and 8 are white. a card will be drawn at random. answer the following questions. write each answer as a fraction. (a) what is the probability that the card drawn is white? (b) what is the probability that the card drawn is white, given that the number drawn is less than 9?

Explanation:

Part (a)

Step1: Identify total and white cards

Total cards: \( 10 \) (numbered 1–10).
White cards: 2, 3, 4, 6, 7, 8 → count = \( 6 \).

Step2: Calculate probability

Probability = \( \frac{\text{White cards}}{\text{Total cards}} = \frac{6}{10} = \frac{3}{5} \).

Step1: Identify restricted sample space

Numbers less than 9: 1, 2, 3, 4, 5, 6, 7, 8 → total = \( 8 \) cards.

Step2: Identify white cards in this space

White cards (from step1): 2, 3, 4, 6, 7, 8 → count = \( 6 \).

Step3: Calculate conditional probability

Probability = \( \frac{\text{White cards in restricted space}}{\text{Restricted space total}} = \frac{6}{8} = \frac{3}{4} \).

Answer:

\( \frac{3}{5} \)

Part (b)