Let's solve each problem one by one.

Question 5

A box contains 3 blue, 2 white, and 4 red marbles.

• Total marbles = 3 (blue) + 2 (white) + 4 (red) = 9 marbles.

(a) Probability of drawing a white marble = $P(\text{white}) = \frac{2}{9}$

(b) Probability of drawing a blue marble = $P(\text{blue}) = \frac{3}{9} = \frac{1}{3}$

(c) Probability of drawing a red marble = $P(\text{red}) = \frac{4}{9}$

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Question 6

A die is thrown once. The possible outcomes are {1, 2, 3, 4, 5, 6}.

(a) Probability of getting a prime number (prime numbers between 1 and 6 are 2, 3, and 5): $P(\text{prime}) = \frac{3}{6} = \frac{1}{2}$

(b) Probability of getting a number between 2 and 6 (inclusive) {3, 4, 5}: $P(\text{between 2 and 6}) = \frac{5}{6}$

(c) Probability of getting an odd number (odd numbers are 1, 3, 5): $P(\text{odd}) = \frac{3}{6} = \frac{1}{2}$

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Question 7

A bag contains 3 red balls and 5 black balls.

• Total balls = 3 (red) + 5 (black) = 8 balls.

(a) Probability of drawing a red ball = $P(\text{red}) = \frac{3}{8}$

(b) Probability of not drawing a red ball (which means drawing a black ball) = $P(\text{not red}) = \frac{5}{8}$

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Question 8

A box contains 5 red marbles, 8 white marbles, and 4 green marbles.

• Total marbles = 5 (red) + 8 (white) + 4 (green) = 17 marbles.

(a) Probability of drawing a red marble = $P(\text{red}) = \frac{5}{17}$

(b) Probability of drawing a white marble = $P(\text{white}) = \frac{8}{17}$

(c) Probability of drawing a marble that is not green (red or white) = $P(\text{not green}) = \frac{5 + 8}{17} = \frac{13}{17}$

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Question 9

A bag has 4 red balls and 2 yellow balls.

• Total balls = 4 (red) + 2 (yellow) = 6 balls.

Probability of drawing a red ball = $P(\text{red}) = \frac{4}{6} = \frac{2}{3}$

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Question 10

Cards are marked with numbers from 1 to 25.

• Total cards = 25.

(a) Probability of drawing a prime number (prime numbers between 1 and 25 are 2, 3, 5, 7, 11, 13, 17, 19, 23): $P(\text{prime}) = \frac{9}{25}$

(b) Probability of drawing an even number (even numbers are {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}): $P(\text{even}) = \frac{12}{25}$

(c) Probability of drawing a multiple of 5 (multiples of 5 between 1 and 25 are {5, 10, 15, 20, 25}): $P(\text{multiple of 5}) = \frac{5}{25} = \frac{1}{5}$

(d) Probability of drawing a number divisible by 6 (multiples of 6 between 1 and 25 are {6, 12, 18}): $P(\text{divisible by 6}) = \frac{3}{25}$

(e) Probability of drawing the number 4: $P(\text{4}) = \frac{1}{25}$

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Do you have any questions or need further details? Here are 5 related questions to explore further:

1. What is the probability of drawing two blue marbles consecutively without replacement from Question 5?
2. In Question 6, what is the probability of getting a number greater than 4?
3. What would the probability be in Question 7 if two balls were drawn with replacement?
4. For Question 8, what is the probability of drawing a marble that is neither red nor white?
5. In Question 10, what is the probability of drawing a card that is either even or a multiple of 5?

Tip: When calculating probability, always ensure that the events considered are mutually exclusive (can't happen at the same time) when adding probabilities together.