Question: Probability Practice
Round all results to four decimal places.
1. In a pool, respondents were asked whether they had ever been in a car accident. 363 respondents indicated that they had been in a car accident and 152 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident?
n = 515
363/515 = 0.7049
P(C) = 0.7049
position_hint: top-right
2. The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major Frequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Business 1676
Engineering 938
What is the probability that a randomly selected degree is in English or Mathematics?
0.4501
P(E or M) = (2073 + 2164) / 9383 = 0.4501
position_hint: center
3. Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.229. Find the probability that it will not snow on January 1st in that town.
1 - P(0.229) = 0.771
P(S') = 0.229
P(S') = 0.771
position_hint: bottom-leftUser: Can you hell me with this too?
1. **Problem:** Find the probability that a randomly selected respondent has been in a car accident.
2. **Formula:** Probability $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$
3. **Given:** Number of respondents who had an accident = $363$, total respondents = $363 + 152 = 515$
4. **Calculation:**
$$P(\text{car accident}) = \frac{363}{515}$$
5. **Simplify:**
$$P(\text{car accident}) = 0.7049$$
6. **Answer:** The probability that a randomly selected respondent has been in a car accident is $0.7049$.
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1. **Problem:** Find the probability that a randomly selected degree is in English or Mathematics.
2. **Formula:** For mutually exclusive events $E$ and $M$,
$$P(E \text{ or } M) = P(E) + P(M) = \frac{\text{Frequency of } E}{\text{Total}} + \frac{\text{Frequency of } M}{\text{Total}}$$
3. **Given:** Frequencies: English = $2073$, Mathematics = $2164$, Total degrees = $2073 + 2164 + 318 + 856 + 1358 + 1676 + 938 = 9383$
4. **Calculation:**
$$P(E \text{ or } M) = \frac{2073 + 2164}{9383}$$
5. **Simplify:**
$$P(E \text{ or } M) = \frac{4237}{9383} = 0.4501$$
6. **Answer:** The probability that a randomly selected degree is in English or Mathematics is $0.4501$.
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1. **Problem:** Find the probability that it will not snow on January 1st.
2. **Formula:** Complement rule:
$$P(S') = 1 - P(S)$$
3. **Given:** $P(S) = 0.229$
4. **Calculation:**
$$P(S') = 1 - 0.229$$
5. **Simplify:**
$$P(S') = 0.771$$
6. **Answer:** The probability that it will not snow on January 1st is $0.771$.