Question

At a small four-year college, all freshmen and sophomores are required to enroll in exactly one of the

following math classes: Math I, Math II or Math III. 200 freshmen and 450 sophomores are enrolled in Math I, 350 freshmen and 400 sophomores are enrolled in Math II, and 250 freshmen and 300 sophomores are enrolled in Math III.

a) Find the probability that a randomly chosen person is either a freshman or enrolled in Math II.

Please show all work and explain in detail thanks

Answer 1

SOLUTION :

We can make the following table :

                                   Math I          Math II       Math III        Total

Freshmen                  200               350             250              800

Sophomores             450               400             300             1150

_______________________________________________________

 

Total                           650              750              550            1950

_______________________________________________________

So, 

N(Freshmen) = 800

N(Math II) = 750 

Total enrolment = 1950

N (Freshmen OR Math ii) 

= N(Freshmen) + N(Math II) - N(Freshman and Math ii)

= 800 + 750 - 350

= 1200 

So,

P(Freshmen or Math ii) 

= N(Freshmen or Math II) /  N(Total enrolment)

= 1200 / 1950 

= 24 / 39 = 0.6154 (ANSWER).

Answer 2

Answer 3

A U.S. company owns an 80% interest in a company located on Mars. Martian currency is called the Martian Credit. During the year the parent company sold inventory that had cost $24,500 to the subsidiary on account for $28,500 when the exchange rate was $0.5192. The subsidiary still held one-half of the inventory and had not paid the parent company for the purchase at the end of the fiscal period. The unsettled account is denominated in dollars. The exchange rate at the fiscal year-end was $0.4994. Answer: 0.6154

Answer 4

To find the probability that a randomly chosen person is either a freshman or enrolled in Math II, we can use the principle of inclusion-exclusion.

Let's define the following events: F = being a freshman M2 = being enrolled in Math II

We are looking for the probability of the event F ∪ M2 (union of events F and M2).

The probability of a randomly chosen person being a freshman is given by the number of freshmen divided by the total number of students:

P(F) = (Number of freshmen) / (Total number of students)

The probability of a randomly chosen person being enrolled in Math II is given by the number of students enrolled in Math II divided by the total number of students:

P(M2) = (Number of students enrolled in Math II) / (Total number of students)

However, we need to be careful because some students might be counted twice (both as freshmen and enrolled in Math II) when calculating P(F) + P(M2). To correct this, we need to subtract the probability of being both a freshman and enrolled in Math II:

P(F ∩ M2) = (Number of freshmen enrolled in Math II) / (Total number of students)

Now, we can calculate the probability of being either a freshman or enrolled in Math II using the principle of inclusion-exclusion:

P(F ∪ M2) = P(F) + P(M2) - P(F ∩ M2)

Let's plug in the given numbers:

Number of freshmen = 200 Number of students enrolled in Math II = 350 + 400 = 750 Total number of students = 200 + 450 + 350 + 400 + 250 + 300 = 2000 Number of freshmen enrolled in Math II = 350

Now, let's calculate the probability:

P(F) = 200 / 2000 = 0.1 P(M2) = 750 / 2000 = 0.375 P(F ∩ M2) = 350 / 2000 = 0.175

P(F ∪ M2) = 0.1 + 0.375 - 0.175 = 0.3

So, the probability that a randomly chosen person is either a freshman or enrolled in Math II is 0.3 or 30%.