Answers and Step-by-step explanations:
Start at the first box that says "start":
1) The probability of landing on "N" is 1/7 (because there are 7 sectors and only 1 with N on it) and the probability of landing on a vowel is 3/7 (because there are 7 sectors and 3 vowels). Multiplying these, we get 3/49. So, go down the path with 3/49 on it.
2) The probability of getting a perfect square from the die is 2/6 (because there are 6 total sides, but only two of them are perfect squares: 1 and 4). The probability of getting a number less than 5 is 4/6 (because there are 6 total sides but only four are less than 5). Multiplying these, we get 8/36 = 2/9. So, go down the path with 2/9 on it.
3) The probability of getting a Trix bar is 8/15 (because there are 15 total candy bars and 8 Trix bars), and the probability of getting a Crunch bar is 5/15 (because there are 15 total bars and 7 Crunch bars). Multiplying these, we get 40/225 = 8/45. So, go down the path with 8/45 on it.
4) The probability of getting a head is 1/2. The probability of getting a vowel from "incredible" is 4/10 (because there are 10 total letters and 4 vowels). Multiplying these, we get 4/20 = 1/5. So, go down the path with 1/5 on it.
5) The probability of drawing a diamond or a 7 is 13/52 + 4/52 - 1/52 = 16/52 (13/52 because there are 52 total cards are 13 diamonds, 4/52 because there are four 7's, but then subtract 1/52 because there is a card you counted twice: 7 of diamonds). The probability of choosing November is 1/12. Multiplying these, you get 1/39. So, go down the path with the 1/39 on it.
6) Sarah's probability of getting a strike is 5/18, while David's is 9/25. Multiplying these, we get 45/450 = 1/10. So, go down the path with the 1/10 on it.
7) The probability that the first duck is a winner is 25/75. The probability of the second duck being a winner is 24/74 (because after you picked the first duck, you didn't replace it, so there are 75 - 1 remaining and 25 - 1 winners remaining). Multiplying these, we get 4/37. So, go down the path with the 4/37 on it.
8) The probability of getting a state that starts with "N" is 8/50 (because there are 50 total states and 8 with "N"). The probability of getting a number at least 2 is 5/6. Multiplying these, we get 2/15. So, go down the path with 2/15 on it.
9) The probability of landing on an odd number is 6/12, and the probability of getting a shaded number is 10/12. Multiplying these, we get 60/144 = 5/12. So, go down the path with 5/12 on it.
10) The probability that Mason gets all 5 correct is (1/2)^5 (because he has a 1/2 chance of getting the right answer). So, go down the path that says 1/32.
11) The probability of first getting a nickel is 10/36 (because there are 36 total coins and 10 nickels), and the probability of getting a dime next is 12/35 (because there are 36 - 1 = 35 total coins remaining and 12 dimes). Multiplying these, we get 2/21. So, go down the path that says 2/21.
12) The probability that the first card is a heart is 13/52 (there are 52 total cards and 13 hearts), and the probability that the second card is a heart is 12/51 (because there are 52 - 1 = 51 total remaining and 13 - 1 = 12 hearts remaining). Multiplying these, we get 1/17. So, go down the path that says 1/17.
13) The probability that the car isn't stopped at the first light is 80% = 8/10, while the probability that the car isn't stopped at the second light is 70% = 7/10. Multiplying these, we get 14/25. And, that's the end!
Hope this helps!
