The hostel caretaker found a library card at the hostel gate. What is the probability as a percentage, that…

Question

The hostel caretaker found a library card at the hostel gate. What is the probability as a percentage, that it belongs to a learner in Block A? Round off your answer to the nearest percentage.

ScanSolve AI Tutor · Accepted Answer

let's tackle these questions about the hostel layout.

2.1.1 Write down the number of the room labelled A.
The room is explicitly labelled with the letter A in the diagram.
The number of the room labelled A is $\boxed{\text{A}}$ .

2.1.2 Kitso is staying at B07. Explain what B07 mean in this context.
The hostel has 12 identical blocks labelled A to L. B07 means that Kitso is staying in Block B, specifically in Room 07 within that block.

2.1.3 Write a set of directions to walk from room 04 to room 07.

Locate Room 04 and Room 07 on the layout.
Room 04 is on the bottom row, and Room 07 is on the top row, far left.
Provide directions.
From Room 04, exit into the central corridor. Turn left and walk past the unlabelled room, the Bathroom, and the Toilets. Then, turn left again to enter Room 07.

2.1.4 The hostel matron states that the total number of learners in the hostel if ALL the rooms are fully occupied is 192. Verify, showing ALL calculations whether her statement is CORRECT.
Determine the number of rooms in one block from the layout.
The layout for Block A shows 6 rooms: Room 07, Room A, Room 03, Room 01, Room 04, and Room 02.
Calculate the total number of beds in one block.
Room 07 has 4 beds. The other 5 rooms (A, 01, 02, 03, 04) each have 3 beds.
$\text{Beds per block} = 4 \text{ (for Room 07)} + (5 \text{ rooms} \times 3 \text{ beds/room})$ $\text{Beds per block} = 4 + 15 = 19 \text{ beds}$
Calculate the total number of learners in the hostel.
There are 12 identical blocks.
$\text{Total learners} = 12 \text{ blocks} \times 19 \text{ beds/block}$ $\text{Total learners} = 228 \text{ learners}$
Compare with the matron's statement.
The matron states 192 learners, but the calculation shows 228 learners.
Therefore, the matron's statement is $\boxed{\text{INCORRECT}}$ .

2.1.5 Explain the meaning of the scale 1 : 150.
A scale of 1:150 means that every 1 unit of measurement on the layout or drawing represents 150 of the same units in actual size. For example, 1 mm on the plan is 150 mm in reality.

2.1.6 The actual width of bedroom 07 is 3,6 m. Use the given scale to calculate the bedroom width on the layout in mm.
Convert the actual width to millimetres.
$3.6 \text{ m} = 3.6 \times 1000 \text{ mm} = 3600 \text{ mm}$
Use the scale to find the width on the layout.
$\text{Layout width} = \frac{\text{Actual width}}{\text{Scale factor}}$ $\text{Layout width} = \frac{3600 \text{ mm}}{150}$ $\text{Layout width} = 24 \text{ mm}$
The bedroom width on the layout is $\boxed{24 \text{ mm}}$ .

2.2 The hostel caretaker found a library card at the hostel gate. What is the probability as a percentage, that it belongs to a learner in Block A? Round off your answer to the nearest percentage.
Identify the total number of blocks.
There are 12 identical blocks (A to L).
Determine the number of favourable outcomes (card belongs to Block A).
There is 1 Block A.
Calculate the probability.
$\text{Probability} = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{12}$
Convert the probability to a percentage and round.
$\text{Percentage probability} = \frac{1}{12} \times 100\% \approx 8.33\%$
Rounding to the nearest percentage, the probability is $\boxed{8\%}$ .

The hostel caretaker found a library card at the hostel gate. What is the probability as a percentage, that it belongs to a learner in Block A? Round off your answer to the nearest percentage.

Step-by-step solution

Locate Room 04 and Room 07 on the layout.

Provide directions.

Determine the number of rooms in one block from the layout.

Calculate the total number of beds in one block.

Calculate the total number of learners in the hostel.

Compare with the matron's statement.

Convert the actual width to millimetres.

Use the scale to find the width on the layout.

Identify the total number of blocks.

Determine the number of favourable outcomes (card belongs to Block A).

Calculate the probability.

Convert the probability to a percentage and round.

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