- Problem ①: The probability tree correctly represents the spinner being spun twice. The first spin has P(Red) = 3/8 and P(Black) = 5/8. For the second spin, since the spinner is fair and independent, the probabilities remain P(Red) = 3/8 and P(Black) = 5/8 regardless of the first outcome. The tree branches show these conditional probabilities correctly.
- Problem ②: To find the probability Hannah wins at least one match, use the complement rule. P(wins at least one) = 1 - P(loses both). P(lose first) = 1 - 0.8 = 0.2, P(lose second) = 1 - 0.6 = 0.4. Assuming independence, P(lose both) = 0.2 × 0.4 = 0.08. Therefore, P(wins at least one) = 1 - 0.08 = 0.92.
- Problem ③: Total pens = 20. P(pick black then red) = (15/20) × (5/19) = 75/380. P(pick red then black) = (5/20) × (15/19) = 75/380. Since these are mutually exclusive, total P(different colors) = 75/380 + 75/380 = 150/380 = 15/38.
- Problem ④: Initially, 3 black and 2 white discs. P(first disc black) = 3/5; then 6 black, 2 white → P(second black) = 6/8. P(first disc white) = 2/5; then 3 black, 5 white → P(second white) = 5/8. P(same color) = P(both black) + P(both white) = (3/5)(6/8) + (2/5)(5/8) = 18/40 + 10/40 = 28/40 = 7/10.
Parent Tip: Review the logic above to help your child master the concept of probability tree diagrams worksheets.
