the probability that a first - year student entering a certain private college needs neither a developmental…

the probability that a first - year student entering a certain private college needs neither a developmental math course nor a developmental english is 67%. while 26% 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.

the probability that a first - year student entering a certain private college needs neither a developmental math course nor a developmental english is 67%. while 26% 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

Explanation:

Step1: Use probability formula

Let (A) be the event of needing developmental math and (B) be the event of needing developmental English. We know (P(A) = 0.26), (P(B)=0.25), and (P((A\cup B)^C)=0.67). First, find (P(A\cup B)) using (P((A\cup B)^C) = 1 - P(A\cup B)). So (P(A\cup B)=1 - 0.67=0.33).

Step2: Apply inclusion - exclusion principle

The inclusion - exclusion principle states that (P(A\cup B)=P(A)+P(B)-P(A\cap B)). We want to find (P(A\cap B)). Rearranging the formula gives (P(A\cap B)=P(A)+P(B)-P(A\cup B)). Substitute (P(A) = 0.26), (P(B)=0.25), and (P(A\cup B)=0.33) into the formula: (P(A\cap B)=0.26 + 0.25- 0.33).

Step3: Calculate the result

(P(A\cap B)=0.18)

Answer:

(0.18)