In a survey a group of students were asked to indicate their favourite soft drink. The result is shown in the…

Question

In a survey a group of students were asked to indicate their favourite soft drink. The result is shown in the table below. (a) How many students are involved in the survey?

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for questions 5 and 6.

Question 5: Probability of Musa and Okeke passing mathematics tests.

Given probabilities:
$P(\text{Musa passes}) = P(M) = 0.75$
$P(\text{Okeke passes}) = P(O) = 0.4$

From these, we can find the probabilities of them failing:
$P(\text{Musa fails}) = P(M') = 1 - P(M) = 1 - 0.75 = 0.25$
$P(\text{Okeke fails}) = P(O') = 1 - P(O) = 1 - 0.4 = 0.6$

a) Draw a tree diagram to illustrate the outcomes of the two independent events.

Start
├── Musa Passes (P=0.75)
│   ├── Okeke Passes (P=0.4)  -> Outcome: (M, O), P = 0.75 * 0.4 = 0.30
│   └── Okeke Fails (P=0.6)   -> Outcome: (M, O'), P = 0.75 * 0.6 = 0.45
└── Musa Fails (P=0.25)
    ├── Okeke Passes (P=0.4)  -> Outcome: (M', O), P = 0.25 * 0.4 = 0.10
    └── Okeke Fails (P=0.6)   -> Outcome: (M', O'), P = 0.25 * 0.6 = 0.15

b) Calculate the probabilities that:

(i) both of them will pass the test

Identify the event.
This means Musa passes AND Okeke passes. Since the events are independent, we multiply their probabilities.
$P(\text{both pass}) = P(M) \times P(O)$
Substitute values and calculate.
$P(\text{both pass}) = 0.75 \times 0.4$ $P(\text{both pass}) = 0.30$
The probability that both of them will pass the test is $\boxed{0.30}$ .

(ii) both of them will fail the test
Identify the event.
This means Musa fails AND Okeke fails. Since the events are independent, we multiply their probabilities of failing.
$P(\text{both fail}) = P(M') \times P(O')$
Substitute values and calculate.
$P(\text{both fail}) = 0.25 \times 0.6$ $P(\text{both fail}) = 0.15$
The probability that both of them will fail the test is $\boxed{0.15}$ .

(iii) only one of them will pass the test
Identify the events.
This can happen in two ways: (Musa passes AND Okeke fails) OR (Musa fails AND Okeke passes). We calculate the probability of each case and add them.
$P(\text{only one passes}) = (P(M) \times P(O')) + (P(M') \times P(O))$
Substitute values and calculate.
$P(\text{only one passes}) = (0.75 \times 0.6) + (0.25 \times 0.4)$ $P(\text{only one passes}) = 0.45 + 0.10$ $P(\text{only one passes}) = 0.55$
The probability that only one of them will pass the test is $\boxed{0.55}$ .

Question 6: Survey on favourite soft drinks.

The table shows the number of students who prefer each drink:
- Coke: 20 students
- Fanta: 15 students
- Sprite: 10 students
- Lemon: 5 students
a) How many students are involved in the survey?
Sum the number of students for each drink.
The total number of students is the sum of all the numbers in the "Numbers" row.
$\text{Total students} = 20 + 15 + 10 + 5$
Calculate the total.
$\text{Total students} = 50$
The total number of students involved in the survey is $\boxed{50}$ .

In a survey a group of students were asked to indicate their favourite soft drink. The result is shown in the table below. (a) How many students are involved in the survey?

Step-by-step solution

Identify the event.

Substitute values and calculate.

Identify the event.

Substitute values and calculate.

Identify the events.

Substitute values and calculate.

Sum the number of students for each drink.

Calculate the total.

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