Complete Two-Way Table and Calculate Random Selection Probability for Year 8 Pupils

Question

100 pupils visited the school library over a four day period. The two way table shows some information about these pupils. a) Complete the two-way table. b) One of the pupils is picked at random to be library monitor. What is the probability they are in year 8?

Accepted Answer

a) Completed table: 
|          | Tuesday | Wednesday | Thursday | Friday | Total |
|----------|---------|-----------|----------|--------|-------|
| Year 7   | 16      | 10        | 11       | 15     | 52    |
| Year 8   | 10      | 7         | 8        | 18     | 48    |
| Total    | 26      | 17        | 24       | 33     | 100   |
b) $\frac{12}{25}$ or 0.48

Answer

Step 1: Calculate missing values for Year 7 first. Total Year 7 pupils = 52. We know Year 7 Tuesday=16, Friday=15, so sum of Wednesday and Thursday Year 7 = 52 - 16 -15 = 21. Thursday total is 24, Year 8 Thursday=8, so Year 7 Thursday = 24 - 8 =11. Then Year 7 Wednesday = 21 -11 =10. Step 2: Calculate Friday Year 8 pupils. Friday total=33, Year7 Friday=15, so Year8 Friday=33-15=18. Step3: Calculate Year8 total. Total pupils=100, Year7 total=52, so Year8 total=100-52=48. Step4: Calculate Year8 Wednesday. Wednesday total=17, Year7 Wednesday=10, so Year8 Wednesday=17-10=7. Step5: Calculate Year8 Tuesday. Year8 total=48, so Year8 Tuesday=48 -7 -8 -18=10. Step6: Calculate Tuesday total. Tuesday total=16+10=26. Step7: For part b, probability a random pupil is Year8 = (Number of Year8 pupils) / (Total pupils) = 48/100 = 12/25.