به انگلیسی

Given that changes everything

Mathematics · Probability · ages 15-16

Name ______________________ Date ____________

A table shows 24 club members, including 9 who cycle. Choose a member uniformly at random. What is P(does not cycle given club member)? Give a decimal.
Answer: ______________
Choose a pupil uniformly at random.
Year Choir No choir Total
10 7 13 ?
11 9 11 20
Total 16 24 40
What is P(choir given Year 10)?
- 7/40
- 7/16
- 13/20
- 7/20
A pupil is selected uniformly at random from a group. For P(tennis given girl), which pupils supply the denominator?
- All girls in the group
- All pupils in the group
- All tennis players in the group
A Venn diagram has A-only 9, both 5 and B-only 6. To find P(A given B) by uniform selection, the denominator counts 11 cases.
Circle one: True False
Choose a student uniformly at random.
Year Chess No chess Total
10 8 12 20
11 12 18 30
12 10 30 40
Total 30 60 90
What is P(chess given Year 10 or Year 11)? Give a decimal.
Answer: ______________
Choose a case uniformly at random. A Venn diagram has A-only 12, both 6, B-only 4 and neither 8. What is P(B given A)?
- 3/5
- 1/3
- 1/5
- 2/3
Choose a case uniformly at random. A Venn diagram has A-only 7, both 0, B-only 9 and neither 4. What is P(A given B)?
- 7/20
- 0
- 7/16
- 1
In a count table, B contains no cases. P(A given B) can be calculated by dividing the overlap count by zero.
Circle one: True False
A made-up inspection gives these counts.
Part Positive Negative Total
Faulty 18 2 20
Sound 42 938 980
Total 60 940 1000
Choose a part uniformly at random. Which calculation finds P(faulty given positive)?
- 18/20, using all faulty parts
- 42/60, counting sound positives
- 18/1000, using all tested parts
- 18/60, using all positive parts
Choose a case uniformly at random. A contains 40 cases, B contains 30, and P(A given B) = 0.4. What is P(B given A)? Give a decimal.
Answer: ______________

Year	Choir	No choir	Total
10	7	13	?
11	9	11	20
Total	16	24	40

Year	Chess	No chess	Total
10	8	12	20
11	12	18	30
12	10	30	40
Total	30	60	90

Part	Positive	Negative	Total
Faulty	18	2	20
Sound	42	938	980
Total	60	940	1000

Answer key

For grown-ups. Fold this page away before handing over the rest.

Given that changes everything W1-mt_Vx88ugViYP-s1

0.625 · There are 24 - 9 = 15 non-cyclists in the given group. Their fraction is 15/24 = 0.625.
7/20 · The Year 10 total is 7 + 13 = 20. Seven sing in choir, giving 7/20.
All girls in the group · The condition is girl, so the denominator counts all girls in the group.
True · B includes the overlap and the B-only region. Its total is 5 + 6 = 11.
0.4 · The two allowed rows contain 20 + 30 = 50 students and 8 + 12 = 20 chess players. Divide 20/50 = 0.4.
1/3 · A contains 12 + 6 = 18 cases. Six also belong to B, so 6/18 = 1/3.
0 · B contains 9 cases, and none belong to A. The probability is 0/9 = 0.
False · The given-group count must be nonzero. With no B cases, the count-based conditional probability is undefined.
18/60, using all positive parts · The given group contains 60 positive parts. Its 18 faulty parts give 18/60 = 0.3.
0.3 · The overlap is 0.4 × 30 = 12 cases. Reverse the condition using A's total: 12/40 = 0.3.