a card is drawn from a standard 52 - card deck. find\n6. p(ace)\n7. p(red)\n8. p(diamond)\n9. p(face)\n10…

a card is drawn from a standard 52 - card deck. find\n6. p(ace)\n7. p(red)\n8. p(diamond)\n9. p(face)\n10. p(2 or 3)\n11. p(black or heart)\n12. p(not a king)\n13. p(not a face)\nthere are 6 red, 3 blue, and 1 white marbles in a jar. find\n14. p(blue)\n15. p(red or white)\n16. p(green)\n17. p(non - white)\n18. p(non - yellow)\na random number from 1 to 20 is drawn from a hat. find\n19. p(7)\n20. p(5 or lower)\n21. p(15 or higher)\n22. p(multiple of 4)\n23. p(even)\n24. p(not a 15)\n25. p(2)

a card is drawn from a standard 52 - card deck. find\n6. p(ace)\n7. p(red)\n8. p(diamond)\n9. p(face)\n10. p(2 or 3)\n11. p(black or heart)\n12. p(not a king)\n13. p(not a face)\nthere are 6 red, 3 blue, and 1 white marbles in a jar. find\n14. p(blue)\n15. p(red or white)\n16. p(green)\n17. p(non - white)\n18. p(non - yellow)\na random number from 1 to 20 is drawn from a hat. find\n19. p(7)\n20. p(5 or lower)\n21. p(15 or higher)\n22. p(multiple of 4)\n23. p(even)\n24. p(not a 15)\n25. p(2)

Answer

  1. Problem 6: P(Ace)

    • Explanation:

      • Step1: Determine number of aces and total cards

        • A standard deck has 52 cards and 4 aces.

      • Step2: Calculate probability

        • The probability formula is (P(E)=\frac{n(E)}{n(S)}), where (n(E)) is the number of favorable - outcomes and (n(S)) is the total number of outcomes. So (P(Ace)=\frac{4}{52}=\frac{1}{13}).

    • Answer: (\frac{1}{13})

  2. Problem 7: P(Red)

    • Explanation:

      • Step1: Determine number of red cards and total cards

        • A standard deck has 52 cards, and 26 of them are red (13 hearts and 13 diamonds).

      • Step2: Calculate probability

        • Using the formula (P(E)=\frac{n(E)}{n(S)}), we have (P(Red)=\frac{26}{52}=\frac{1}{2}).

    • Answer: (\frac{1}{2})

  3. Problem 8: P(Diamond)

    • Explanation:

      • Step1: Determine number of diamonds and total cards

        • A standard deck has 52 cards and 13 diamonds.

      • Step2: Calculate probability

        • By the probability formula (P(E)=\frac{n(E)}{n(S)}), (P(Diamond)=\frac{13}{52}=\frac{1}{4}).

    • Answer: (\frac{1}{4})

  4. Problem 9: P(Face)) (assuming this is a repeat - let's solve it again)

    • Explanation:

      • Step1: Determine number of face - cards and total cards

        • A standard deck has 52 cards. Face - cards are Jacks, Queens, and Kings, with 4 of each type, so there are 12 face - cards.

      • Step2: Calculate probability

        • Using (P(E)=\frac{n(E)}{n(S)}), (P(Face)=\frac{12}{52}=\frac{3}{13}).

    • Answer: (\frac{3}{13})

  5. Problem 10: P(2 or 3)

    • Explanation:

      • Step1: Determine number of 2s and 3s and total cards

        • There are 4 twos and 4 threes in a 52 - card deck, so (n(E)=4 + 4=8).

      • Step2: Calculate probability

        • By the formula (P(E)=\frac{n(E)}{n(S)}), (P(2\ or\ 3)=\frac{8}{52}=\frac{2}{13}).

    • Answer: (\frac{2}{13})

  6. Problem 11: P(Black or Heart)

    • Explanation:

      • Step1: Determine number of black cards, hearts, and subtract double - counted cards

        • There are 26 black cards and 13 hearts in a 52 - card deck. But there are no cards that are both black and heart. So (n(E)=26 + 13=39).

      • Step2: Calculate probability

        • Using (P(E)=\frac{n(E)}{n(S)}), (P(Black\ or\ Heart)=\frac{39}{52}=\frac{3}{4}).

    • Answer: (\frac{3}{4})

  7. Problem 12: P(not a King)

    • Explanation:

      • Step1: Determine number of non - King cards and total cards

        • A standard deck has 52 cards and 4 Kings. So the number of non - King cards is (n(E)=52−4 = 48).

      • Step2: Calculate probability

        • By the formula (P(E)=\frac{n(E)}{n(S)}), (P(not\ a\ King)=\frac{48}{52}=\frac{12}{13}).

    • Answer: (\frac{12}{13})

  8. Problem 13: P(not a Face)

    • Explanation:

      • Step1: Determine number of non - face cards and total cards

        • A standard deck has 52 cards and 12 face - cards. So the number of non - face cards is (n(E)=52−12 = 40).

      • Step2: Calculate probability

        • Using (P(E)=\frac{n(E)}{n(S)}), (P(not\ a\ Face)=\frac{40}{52}=\frac{10}{13}).

    • Answer: (\frac{10}{13})

  9. Problem 14: P(blue) for marbles

    • Explanation:

      • Step1: Determine number of blue marbles and total marbles

        • There are 3 blue marbles, and the total number of marbles is (6 + 3+1=10).

      • Step2: Calculate probability

        • By (P(E)=\frac{n(E)}{n(S)}), (P(blue)=\frac{3}{10}).

    • Answer: (\frac{3}{10})

  10. Problem 15: P(red or white) for marbles

  • Explanation:

    • Step1: Determine number of red and white marbles and total marbles

      • There are 6 red and 1 white marble, so (n(E)=6 + 1=7), and the total number of marbles is 10.

    • Step2: Calculate probability

      • Using (P(E)=\frac{n(E)}{n(S)}), (P(red\ or\ white)=\frac{7}{10}).

  • Answer: (\frac{7}{10})

  1. Problem 16: P(green) for marbles

  • Explanation:

    • Step1: Determine number of green marbles and total marbles

      • There are 0 green marbles and 10 total marbles.

    • Step2: Calculate probability

      • By (P(E)=\frac{n(E)}{n(S)}), (P(green)=\frac{0}{10}=0).

  • Answer: (0)

  1. Problem 17: P(non - white) for marbles

  • Explanation:

    • Step1: Determine number of non - white marbles and total marbles

      • There are (6 + 3=9) non - white marbles and 10 total marbles.

    • Step2: Calculate probability

      • Using (P(E)=\frac{n(E)}{n(S)}), (P(non - white)=\frac{9}{10}).

  • Answer: (\frac{9}{10})

  1. Problem 18: P(non - yellow) for marbles

  • Explanation:

    • Step1: Determine number of non - yellow marbles and total marbles

      • Since there are no yellow marbles among the 10 marbles ((6) red, (3) blue, (1) white), all 10 marbles are non - yellow.

    • Step2: Calculate probability

      • By (P(E)=\frac{n(E)}{n(S)}), (P(non - yellow)=\frac{10}{10}=1).

  • Answer: (1)

  1. Problem 19: P(7) for numbers from 1 to 20

  • Explanation:

    • Step1: Determine number of 7s and total numbers

      • There is 1 number 7 in the set of numbers from 1 to 20, and (n(S)=20).

    • Step2: Calculate probability

      • Using (P(E)=\frac{n(E)}{n(S)}), (P(7)=\frac{1}{20}).

  • Answer: (\frac{1}{20})

  1. Problem 20: P(5 or lower) for numbers from 1 to 20

  • Explanation:

    • Step1: Determine number of numbers 5 or lower and total numbers

      • The numbers 1, 2, 3, 4, 5 are 5 numbers. And (n(S)=20).

    • Step2: Calculate probability

      • By (P(E)=\frac{n(E)}{n(S)}), (P(5\ or\ lower)=\frac{5}{20}=\frac{1}{4}).

  • Answer: (\frac{1}{4})

  1. Problem 21: P(15 or higher) for numbers from 1 to 20

  • Explanation:

    • Step1: Determine number of numbers 15 or higher and total numbers

      • The numbers 15, 16, 17, 18, 19, 20 are 6 numbers. And (n(S)=20).

    • Step2: Calculate probability

      • Using (P(E)=\frac{n(E)}{n(S)}), (P(15\ or\ higher)=\frac{6}{20}=\frac{3}{10}).

  • Answer: (\frac{3}{10})

  1. Problem 22: P(multiple of 4) for numbers from 1 to 20

  • Explanation:

    • Step1: Determine number of multiples of 4 and total numbers

      • The multiples of 4 from 1 to 20 are 4, 8, 12, 16, 20, so (n(E)=5), and (n(S)=20).

    • Step2: Calculate probability

      • By (P(E)=\frac{n(E)}{n(S)}), (P(multiple\ of\ 4)=\frac{5}{20}=\frac{1}{4}).

  • Answer: (\frac{1}{4})

  1. Problem 23: P(even) for numbers from 1 to 20

  • Explanation:

    • Step1: Determine number of even numbers and total numbers

      • There are 10 even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) in the set of numbers from 1 to 20, and (n(S)=20).

    • Step2: Calculate probability

      • Using (P(E)=\frac{n(E)}{n(S)}), (P(even)=\frac{10}{20}=\frac{1}{2}).

  • Answer: (\frac{1}{2})

  1. Problem 24: P(not a 15) for numbers from 1 to 20

  • Explanation:

    • Step1: Determine number of non - 15 numbers and total numbers

      • There are (20−1 = 19) non - 15 numbers in the set of numbers from 1 to 20, and (n(S)=20).

    • Step2: Calculate probability

      • By (P(E)=\frac{n(E)}{n(S)}), (P(not\ a\ 15)=\frac{19}{20}).

  • Answer: (\frac{19}{20})

  1. Problem 25: P(20) for numbers from 1 to 20

  • Explanation:

    • Step1: Determine number of 20s and total numbers

      • There is 1 number 20 in the set of numbers from 1 to 20, and (n(S)=20).

    • Step2: Calculate probability

      • Using (P(E)=\frac{n(E)}{n(S)}), (P(20)=\frac{1}{20}).

  • Answer: (\frac{1}{20})