In Imogen’s class 15 students play tennis, 14 play basketball and 7 play both. Theprobability that a randomly chosen student plays basketball, given that they playtennis, is单项选择题
A
a. 14/15
B
b. 7/15
C
c. 15/29
D
d. 7/29

Question

In Imogen’s class 15 students play tennis, 14 play basketball and 7 play both. Theprobability that a randomly chosen student plays basketball, given that they playtennis, is

BlackTom AI · Accepted Answer

Conditional probability P(Basketball | Tennis) = P(B and T) / P(T). Here counts can be used directly because each student is equally likely to be chosen.

1) Relevant concepts:
- Conditional probability: the probability of event B given event T is the proportion of T-outcomes that also satisfy B.
- When events are described by counts, probabilities = counts / total, and the conditional probability reduces to (number in both) / (number in the conditioning group).

2) Step-by-step reasoning:
- Number of students who play tennis = 15 (this is the conditioning group).
- Number of students who play both tennis and basketball = 7 (these are tennis players who also play basketball).
- The probability that a randomly chosen student plays basketball given they play tennis is the fraction of tennis players who also play basketball:
  P(B | T) = (number who play both) / (number who play tennis).

3) Calculations (intermediate steps shown):
- numerator = 7
- denominator = 15
- P(B | T) = 7 / 15

4) Why this is correct:
- By definition P(B | T) asks: "Out of those who play tennis, what proportion also play basketball?" Exactly 7 of the 15 tennis players do, so the correct probability is 7/15.

5) Why the other options are incorrect:
- a. 14/15 would mean 14 of the 15 tennis players also play basketball, but only 7 do, so 14/15 is too large.
- c. 15/29 uses 29 (15 + 14) as a denominator which double-counts the overlap; it does not represent the number of tennis players and so is not relevant for P(B | T).
- d. 7/29 similarly uses 29 in the denominator and would represent neither P(B | T) nor any meaningful conditional probability here.

6) Conclusion:
The conditional probability is 7/15, which matches the provided correct answer (option b).

In Imogen’s class 15 students play tennis, 14 play basketball and 7 play both. Theprobability that a randomly chosen student plays basketball, given that they playtennis, is单项选择题

类似问题

The Venn diagram below represents 2 events [math: A] and [math: B] as shown. If [math: Pr(A)=0.3] and [math: Pr(B)=0.6], the value of [math: Pr(B|A)] is

______ is the probability of Event Y occurring, given that Event Z has already occurred.

The Venn diagram below represents 2 events [math: A] and [math: B] as shown. If [math: Pr(A)=0.5] and [math: Pr(B)=0.6], the value of [math: Pr(B|A)] is

The Venn diagram below represents 2 events [math: A] and [math: B] as shown. If [math: Pr(A)=0.3] and [math: Pr(B)=0.6], the value of [math: Pr(B|A)] is

The following data was derived from accident records on a highway noted for itsabove-average accident rate. The probability that the accident is not fatal, given that reckless driving is the cause, isclosest to

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单