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单项选择题
A
a. 0.82
B
b. 0.17
C
c. 0.23
D
d. 0.21

Question

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单项选择题

A

a. 0.82

B

b. 0.17

C

c. 0.23

D

d. 0.21

BlackTom AI · Accepted Answer

Conditional probability P(A|B) = P(A and B)/P(B), so to find the probability the accident is non‑fatal given reckless driving we use the reckless‑driving column entries.

1. Relevant knowledge points and concepts
- A contingency table lists joint counts for two categorical variables (type of accident vs probable cause).  
- The conditional probability "non‑fatal | reckless" uses only the cases where the cause is reckless driving.  
- Formula: P(non‑fatal | reckless) = (number of non‑fatal & reckless) / (total number with reckless cause).

2. Step‑by‑step reasoning
- Locate the reckless driving column in the table. The table shows: fatal = 22, non‑fatal = 98, total (reckless) = 120.  
- We want the fraction of reckless‑cause accidents that are non‑fatal, i.e., 98 out of the 120 reckless cases.

3. Calculations (all intermediate steps)
- Fraction: 98 / 120  
- Divide: 98 ÷ 120 = 0.816666...  
- Round to two decimal places (as in the answer choices): 0.816666... ≈ 0.82

4. Why the correct answer is correct
- The conditional probability uses only the 120 reckless cases as the denominator; among those, 98 were non‑fatal. That ratio directly yields ≈0.8167, which matches choice a (0.82) once rounded.

5. Why the other options are incorrect
- b (0.17) is approximately 22/120 = 0.1833 (the fatal proportion given reckless), so it’s the complement, not the asked probability.  
- c (0.23) and d (0.21) do not match any relevant ratio from the reckless column (they would correspond to incorrect divisions or misreading other columns).

6. Conclusion confirming the answer
- Therefore P(non‑fatal | reckless) = 98/120 ≈ 0.82, so the correct choice is a. 0.82.

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单项选择题

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