5.	A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be
(a) white?	(b) blue?	(c) red?
6.	A die is thrown once. Find the probability of getting
(a)	a prime number
(b)	a number lying between 2 and 6
(c)	an odd number.
7.	A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag.
What is the probability that the ball drawn is
(a)	red ?	(b) not red?
8.	A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be
(a) red ?	(b) white ?	(c) not green?
9.	A bag has 4 red balls and 2 yellow balls. A ball is drawn from the bag without looking into the bag. What is probability of getting a red ball?
10.	Cards are marked with numbers 1 to 25 are placed in the box and mixed thoroughly. One card is drawn at random from the box. What is the probability that the cards are marked with
(a)	a prime number
(b)	an even number
(c)	a number multiple of 5
(d)	a number divisible by 6 and
(e)	a number 4.



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 = \( P(\text{red}) = \frac{4}{6} = \frac{2}{3} \)

---

### 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.

5. A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be (a) white? (b) blue? (c) red? 6. A die is thrown once. Find the probability of getting (a) a prime number (b) a number lying between 2 and 6 (c) an odd number. 7. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (a) red ? (b) not red? 8. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (a) red ? (b) white ? (c) not green? 9. A bag has 4 red balls and 2 yellow balls. A ball is drawn from the bag without looking into the bag. What is probability of getting a red ball? 10. Cards are marked with numbers 1 to 25 are placed in the box and mixed thoroughly. One card is drawn at random from the box. What is the probability that the cards are marked with (a) a prime number (b) an even number (c) a number multiple of 5 (d) a number divisible by 6 and (e) a number 4.

This detailed guide covers various probability problems, including drawing marbles from a box, rolling a die for prime numbers, and selecting cards from a set. Learn key probability concepts like favorable outcomes, prime numbers, and calculating event likelihoods. Suitable for Grades 6-8 students.

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