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In a math class of 30 students:
- 15 hate the subject
- 7 dislike it
- 5 like it
- 3 love it

If a student is selected at random from the group, what is the probability that they will:

(a) hate math
(b) dislike math
(c) like math
(d) love math
(e) either hate or dislike math
(f) either love or hate math

200 tickets are sold for a raffle. What is the probability of winning if you buy:

(a) 1 ticket
(b) 5 tickets
(c) 10 tickets
(d) 25 tickets
(e) 200 tickets
(f) 0 tickets



Answer :

GinnyAnswer
Certainly! Let's work through this question step-by-step:

### Part 1: Maths Class

In a maths class of 30 students:
- 15 students hate maths.
- 7 students dislike maths.
- 5 students like maths.
- 3 students love maths.

Let's determine the probabilities.

#### (a) Probability that a student hates maths
This is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students who hate maths}}{\text{Total number of students}} \][/tex]
[tex]\[ \text{Probability} = \frac{15}{30} = 0.5 \][/tex]

#### (b) Probability that a student dislikes maths
This is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students who dislike maths}}{\text{Total number of students}} \][/tex]
[tex]\[ \text{Probability} = \frac{7}{30} = 0.2333 \][/tex] (approximately)

#### (c) Probability that a student likes maths
This is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students who like maths}}{\text{Total number of students}} \][/tex]
[tex]\[ \text{Probability} = \frac{5}{30} = 0.1667 \][/tex] (approximately)

#### (d) Probability that a student loves maths
This is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of students who love maths}}{\text{Total number of students}} \][/tex]
[tex]\[ \text{Probability} = \frac{3}{30} = 0.1 \][/tex]

#### (e) Probability that a student either hates or dislikes maths
This is a combined event, so:
[tex]\[ \text{Probability} = \frac{\text{Number of students who hate maths} + \text{Number of students who dislike maths}}{\text{Total number of students}} \][/tex]
[tex]\[ \text{Probability} = \frac{15 + 7}{30} = \frac{22}{30} = 0.7333 \][/tex] (approximately)

#### (f) Probability that a student either loves or hates maths
This is another combined event, so:
[tex]\[ \text{Probability} = \frac{\text{Number of students who love maths} + \text{Number of students who hate maths}}{\text{Total number of students}} \][/tex]
[tex]\[ \text{Probability} = \frac{3 + 15}{30} = \frac{18}{30} = 0.6 \][/tex]

### Part 2: Raffle Ticket Probability

200 tickets are sold for a raffle. Let's determine the probabilities of winning depending on the number of tickets bought.

#### (a) Probability of winning with 1 ticket
[tex]\[ \text{Probability} = \frac{\text{Number of tickets bought}}{\text{Total number of tickets}} \][/tex]
[tex]\[ \text{Probability} = \frac{1}{200} = 0.005 \][/tex]

#### (b) Probability of winning with 5 tickets
[tex]\[ \text{Probability} = \frac{5}{200} = 0.025 \][/tex]

#### (c) Probability of winning with 10 tickets
[tex]\[ \text{Probability} = \frac{10}{200} = 0.05 \][/tex]

#### (d) Probability of winning with 25 tickets
[tex]\[ \text{Probability} = \frac{25}{200} = 0.125 \][/tex]

#### (e) Probability of winning with 200 tickets (buying all tickets)
[tex]\[ \text{Probability} = \frac{200}{200} = 1.0 \][/tex]

#### (f) Probability of winning with 0 tickets
[tex]\[ \text{Probability} = \frac{0}{200} = 0 \][/tex]

So, summarized:
- Probability a student hates maths: 0.5
- Probability a student dislikes maths: 0.2333
- Probability a student likes maths: 0.1667
- Probability a student loves maths: 0.1
- Probability a student either hates or dislikes maths: 0.7333
- Probability a student either loves or hates maths: 0.6
- Probability of winning with 1 ticket: 0.005
- Probability of winning with 5 tickets: 0.025
- Probability of winning with 10 tickets: 0.05
- Probability of winning with 25 tickets: 0.125
- Probability of winning with 200 tickets: 1.0
- Probability of winning with 0 tickets: 0

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