90 men and 80 women are enrolled in calculus. There are 40 business majors, 20 biology majors, 55 computer science majors, and 55 mathematics
majors. No person has a double major. If a single calculus student is chosen, find the following probabilites.
Find the probability that the student is a man.
P (man)
(Type an integer or a simplified fraction.)
Find the probability that the student is a mathematics major
P (mathematics)
(Type an integer or a simplified fraction.)
Find the probability that the student is not a computer science major.
P(not computer science)
(Type an integer or a simplified fraction.)
Find the probability that the student is a mathematics major or a computer science major.
P(mathematics computer science)
(Type an integer or a simplified fraction.)

Ask by Mullins Stephens. in the United States

Jan 20,2025

Question

90 men and 80 women are enrolled in calculus. There are 40 business majors, 20 biology majors, 55 computer science majors, and 55 mathematics
majors. No person has a double major. If a single calculus student is chosen, find the following probabilites.
Find the probability that the student is a man.
P (man)
(Type an integer or a simplified fraction.)
Find the probability that the student is a mathematics major
P (mathematics)
(Type an integer or a simplified fraction.)
Find the probability that the student is not a computer science major.
P(not computer science)
(Type an integer or a simplified fraction.)
Find the probability that the student is a mathematics major or a computer science major.
P(mathematics computer science)
(Type an integer or a simplified fraction.)

Ask by Mullins Stephens. in the United States

Jan 20,2025

UpStudy AI · Accepted Answer

To find the probability that a randomly chosen calculus student is either a mathematics major or a computer science major, we can use the following information:

- **Total number of students**: $$ 90 \text{ men} + 80 \text{ women} = 170 \text{ students} $$
- **Mathematics majors**: 55
- **Computer science majors**: 55

Since no student has a double major, the events are mutually exclusive. Therefore, the probability $$ P(\text{mathematics} \cup \text{computer science}) $$ is the sum of the probabilities of each individual event.

$$
P(\text{mathematics} \cup \text{computer science}) = P(\text{mathematics}) + P(\text{computer science})
$$

$$
P(\text{mathematics} \cup \text{computer science}) = \frac{55}{170} + \frac{55}{170} = \frac{110}{170}
$$

Simplifying the fraction:

$$
\frac{110}{170} = \frac{11}{17}
$$

**Final Answer:**

$$
P(\text{mathematics} \cup \text{computer science}) = \frac{11}{17}
$$

Answer: $$ \frac{11}{17} $$
The probability that the student is a mathematics major or a computer science major is $$ \frac{11}{17} $$.

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