Question

The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 70% while 22% require a developmental math course and 25% require a developmental English course. Find the probability that a first year student requires both a development math course and a developmental English course.

Answer 1

The probability that a first year student requires both a developmental math course and a developmental English course is -0.23 or 23%.

Step-by-step explanation:

To find the probability that a first-year student requires both a developmental math course and a developmental English course, we can use the formula:

P(A and B) = P(A) + P(B) - P(A or B)

Given that the probability of needing neither course is 0.70, the probability of needing a developmental math course is 0.22, and the probability of needing a developmental English course is 0.25, we can substitute these values into the formula:

P(Developmental Math and English) = P(Developmental Math) + P(Developmental English) - P(Neither)

P(Developmental Math and English) = 0.22 + 0.25 - 0.70

P(Developmental Math and English) = 0.47 - 0.70

P(Developmental Math and English) = -0.23

Therefore, the probability that a first-year student requires both a developmental math course and a developmental English course is -0.23 or 23%.

Answer 2

Probability of both English and Maths = 17%

Step-by-step explanation:

Probability of English or Maths

100 -70 = 30%

Probability of English or Maths =

Probability of English + Probability of Maths + Probability of both English and Maths

30 % = 22% + 25 % + Probability of both English and Maths

Probability of both English and Maths = 47% - 30 %

Probability of both English and Maths = 17%