Complete the following table to show all of her possible totals.

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Complete the following table to show all of her possible totals - OCR - GCSE Maths - Question 17 - 2020 - Paper 1

Question 17

Complete the following table to show all of her possible totals. | Total | 2 | 2 | 3 | 5 | 6 | |-------|---|---|---|---|---| | Second card | 3 | 5 | 5 | 8 | 9 | | 5... show full transcript

Worked Solution & Example Answer:Complete the following table to show all of her possible totals - OCR - GCSE Maths - Question 17 - 2020 - Paper 1

Step 1

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Answer

To complete the table, we need to add the numbers from the 'First card' and 'Second card' at each intersection. The completed table should display the following:

Total	2	2	3	5	6
Second card	3	5	5	8	9
----------------	---	---	---	---	---
5	7	8	10	11
6	8	9	11	12

So, the totals in the table will be calculated as:

For First card 2:
- Second card 3: 2 + 3 = 5
- Second card 5: 2 + 5 = 7
- Second card 5: 2 + 5 = 7
- Second card 8: 2 + 8 = 10
- Second card 9: 2 + 9 = 11
For First card 2 (second instance): (Similar calculations applying)
For First card 3: (Similar calculations applying)
For First card 5: (Similar calculations applying)
For First card 6: (Similar calculations applying)

After filling in all cards, we get:

Total	2	2	3	5
3	5	5	8	9
5	7	8	10	11
6	8	9	11	12

Step 2

Find the probability that her total is an even number.

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Answer

To find the probability that her total is an even number, we first tally the possible totals from the completed table:

Possible totals: 5, 7, 10, 11, 12

The even totals are: 10, 12. Hence, we have 2 even outcomes out of 6 possibilities.

Thus, the probability $P$ can be calculated using the formula:

$P(Even ext{ Total}) = \frac{Number ext{ of Even Totals}}{Total ext{ Outcomes}} = \frac{2}{6} = \frac{1}{3}.$

Therefore, the probability that her total is an even number is $\frac{1}{3}$ .

Step 3

Find the probability that her total is a multiple of 3 or 4.

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Answer

Again, we will use the totals from the completed table. The multiples of 3 or 4 from our totals:

Possible totals: 5, 7, 10, 11, 12

Multiples of 3: 6, 9, 12 Multiples of 4: 4, 8, 12 Among the totals, the ones that are either multiples of 3 or 4 are: 10, 12.

This gives us a total of 3 favorable outcomes.

Thus, we can calculate the probability:

$P(Multiple ext{ of 3 or 4}) = \frac{Number \text{ of Favorable Outcomes}}{Total \text{ Outcomes}} = \frac{3}{6} = \frac{1}{2}.$

Hence, the probability that her total is a multiple of 3 or 4 is $\frac{1}{2}$ .

Complete the following table to show all of her possible totals - OCR - GCSE Maths - Question 17 - 2020 - Paper 1

Worked Solution & Example Answer:Complete the following table to show all of her possible totals - OCR - GCSE Maths - Question 17 - 2020 - Paper 1