1. For rolling a 6 - sided die:
   • 1. (P(\text{roll a }5)):

     • Explanation:

       Step1: Determine total outcomes

       A 6 - sided die has 6 possible outcomes ((n = 6)).

       Step2: Determine favorable outcomes

       There is 1 way to roll a 5 ((m = 1)). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{roll a }5)=\frac{1}{6}).

     Answer: (\frac{1}{6})

   • 2. (P(\text{roll a }1\text{ or }6)):

     • Explanation:

       Step1: Determine total outcomes

       A 6 - sided die has (n = 6) possible outcomes.

       Step2: Determine favorable outcomes

       There is 1 way to roll a 1 and 1 way to roll a 6, so (m=1 + 1=2). Using the probability formula (P(A)=\frac{m}{n}), we get (P(\text{roll a }1\text{ or }6)=\frac{2}{6}=\frac{1}{3}).

     Answer: (\frac{1}{3})

   • 3. (P(\text{odd }#)):

     • Explanation:

       Step1: Determine total outcomes

       (n = 6) (6 possible outcomes for a 6 - sided die).

       Step2: Determine favorable outcomes

       The odd numbers on a 6 - sided die are 1, 3, and 5, so (m = 3). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{odd }#)=\frac{3}{6}=\frac{1}{2}).

     Answer: (\frac{1}{2})

   • 4. (P(\text{multiple of }3)):

     • Explanation:

       Step1: Determine total outcomes

       (n = 6).

       Step2: Determine favorable outcomes

       The multiples of 3 on a 6 - sided die are 3 and 6, so (m = 2). Using the probability formula (P(A)=\frac{m}{n}), we get (P(\text{multiple of }3)=\frac{2}{6}=\frac{1}{3}).

     Answer: (\frac{1}{3})

   • 5. (P(\text{not a }4)):

     • Explanation:

       Step1: Determine total outcomes

       (n = 6).

       Step2: Determine non - favorable outcomes

       There is 1 way to roll a 4. So the number of non - 4 outcomes (m=6 - 1 = 5). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{not a }4)=\frac{5}{6}).

     Answer: (\frac{5}{6})

2. For drawing a card from a standard 52 - card deck:
   • 6. (P(\text{Ace})):

     • Explanation:

       Step1: Determine total outcomes

       There are (n = 52) cards in a standard deck.

       Step2: Determine favorable outcomes

       There are 4 aces in a deck ((m = 4)). Using the probability formula (P(A)=\frac{m}{n}), we get (P(\text{Ace})=\frac{4}{52}=\frac{1}{13}).

     Answer: (\frac{1}{13})

   • 7. (P(\text{Red})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 52).

       Step2: Determine favorable outcomes

       There are 26 red cards (13 hearts and 13 diamonds) in a deck, so (m = 26). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{Red})=\frac{26}{52}=\frac{1}{2}).

     Answer: (\frac{1}{2})

   • 8. (P(\text{Diamond})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 52).

       Step2: Determine favorable outcomes

       There are 13 diamonds in a deck, so (m = 13). Using the probability formula (P(A)=\frac{m}{n}), we get (P(\text{Diamond})=\frac{13}{52}=\frac{1}{4}).

     Answer: (\frac{1}{4})

   • 9. (P(\text{Face})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 52).

       Step2: Determine favorable outcomes

       Face - cards are Jacks, Queens, and Kings. There are 3 face - card types and 4 suits, so (m = 12). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{Face})=\frac{12}{52}=\frac{3}{13}).

     Answer: (\frac{3}{13})

   • 10. (P(2\text{ or }3)):

     • Explanation:

       Step1: Determine total outcomes

       (n = 52).

       Step2: Determine favorable outcomes

       There are 4 twos and 4 threes in a deck. So (m=4 + 4=8). Using the probability formula (P(A)=\frac{m}{n}), we get (P(2\text{ or }3)=\frac{8}{52}=\frac{2}{13}).

     Answer: (\frac{2}{13})

   • 11. (P(\text{Black or Heart})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 52).

       Step2: Determine favorable outcomes

       There are 26 black cards and 13 hearts. But we need to avoid double - counting. Since hearts are red, there is no overlap. So (m=26 + 13=39). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{Black or Heart})=\frac{39}{52}=\frac{3}{4}).

     Answer: (\frac{3}{4})

   • 12. (P(\text{not a King})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 52).

       Step2: Determine non - favorable outcomes

       There are 4 kings in a deck. So the number of non - king cards (m=52 - 4 = 48). Using the probability formula (P(A)=\frac{m}{n}), we get (P(\text{not a King})=\frac{48}{52}=\frac{12}{13}).

     Answer: (\frac{12}{13})

   • 13. (P(\text{not a Face})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 52).

       Step2: Determine non - favorable outcomes

       There are 12 face cards. So the number of non - face cards (m=52 - 12 = 40). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{not a Face})=\frac{40}{52}=\frac{10}{13}).

     Answer: (\frac{10}{13})

3. For marbles in a jar ((6) red, (3) blue, and (1) white):
   • 14. (P(\text{blue})):

     • Explanation:

       Step1: Determine total outcomes

       The total number of marbles (n=6 + 3+1=10).

       Step2: Determine favorable outcomes

       There are 3 blue marbles ((m = 3)). Using the probability formula (P(A)=\frac{m}{n}), we get (P(\text{blue})=\frac{3}{10}).

     Answer: (\frac{3}{10})

   • 15. (P(\text{red or white})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 10).

       Step2: Determine favorable outcomes

       There are 6 red and 1 white marble, so (m=6 + 1=7). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{red or white})=\frac{7}{10}).

     Answer: (\frac{7}{10})

   • 16. (P(\text{green})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 10).

       Step2: Determine favorable outcomes

       There are 0 green marbles ((m = 0)). Using the probability formula (P(A)=\frac{m}{n}), we get (P(\text{green})=\frac{0}{10}=0).

     Answer: (0)

   • 17. (P(\text{non - white})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 10).

       Step2: Determine non - white outcomes

       There is 1 white marble. So the number of non - white marbles (m=10 - 1 = 9). Using the probability formula (P(A)=\frac{m}{n}), we have (P(\text{non - white})=\frac{9}{10}).

     Answer: (\frac{9}{10})

   • 18. (P(\text{non - yellow})):

     • Explanation:

       Step1: Determine total outcomes

       (n = 10).

       Step2: Determine non - yellow outcomes

       There are 0 yellow marbles. So all 10 marbles are non - yellow ((m = 10)). Using the probability formula (P(A)=\frac{m}{n}), we get (P(\text{non - yellow})=\frac{10}{10}=1).

     Answer: (1)

4. For drawing a random number from 1 to 20:
   • Since the remaining questions (19 - 25) are not fully visible, we will assume a general approach for probability calculations similar to the above. For example, if we consider (P(7)):

     • Explanation:

       Step1: Determine total outcomes

       There are (n = 20) possible numbers from 1 to 20.

       Step2: Determine favorable outcomes

       There is 1 way to get a 7 ((m = 1)). Using the probability formula (P(A)=\frac{m}{n}), we have (P(7)=\frac{1}{20}).

     Answer: (\frac{1}{20})

These are probability problems related to different sample spaces (dice - rolling, card - drawing, marble - picking, and number - drawing), and the solutions are based on the basic probability formula (P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}).