To graduate this semester, you must pass Statistics 314; and you estimate that you have an 85% chance of passing. You need to pass Math 272 or Math 444, each of which you have an 80% chance of passing: so you will take both in hopes that you will pass at least one. Further, you must pass German 320, which you believe you have a 90% chance of passing. Assuming your chances of passing each class you take are independent, what is your probability of graduating this semester

Probability of graduating this semester is 0.7344

Step-by-step explanation:

Given the data in the question;

let A represent passing STAT-314

B represent passing at least in MATH-272 or MATH-444

M1 represent passing in MATH-272

M2 represent passing in MATH-444

C represent  passing GERMAN-32

now

P( A ) = 0.85, P( C ) = 90, P( M1 ) = P( M2 ) = 0.8

P( B ) = P( pass at least one of either MATH-272 or MATH-444 ) = P( pass in MATH-272 but not MATH-444 ) + ( pass in MATH-444 but not in MATH 272) + P( pass both )

P( B ) =  P( M1 ) × ( 1 - P( M2 ) ) + ( 1 - P( M1 ) ) × P( M2 ) + P( M1 ) × P( M2 )

we substitute

⇒ 0.8×0.2 + 0.2×0.8 + 0.8×0.8 = 0.16 + 0.16 + 0.64 = 0.96

∴ the probability of graduating this semester will be;

⇒ P( A ) × P( B ) × P( C )

we substitute

⇒ 0.85 × 0.96 × 90

⇒ 0.7344

Probability of graduating this semester is 0.7344

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: