1 ) Consider a class containing exactly 4 freshmen men, 6 freshmen women, 6 soph

ID: 2959643 • Letter: 1

Question

1) Consider a class containing exactly 4 freshmen men, 6 freshmen women, 6 sophomore men, and f

sophomore women, and consider selecting a student at random from this class. What must the value of

be in order for the event that the student is a female to be independent of the event that the student is a

sophomore?

2)Suppose missile 1 will hit a target with probability 0.1, and missile 2 will hit a target with probability

0.2, and the two missiles hit or don’t hit independently. What is the probability that missile 1 will hit the

target given that at least one of the two missiles hit the target?

1) let event A= the stduent is a female

event B = the student is a sophomore.

event A and event B are indepent if and only if P(A n B) = P(A)P(B)

freshman sophomore

male 4 6

female 6 f

P(A n B) = f / (16+f)

P(A) = (6+f)/(16+f)

P(B) = (6+f)/(16+f)

f/(16+f) = (6+f)2/(16+f)2

simplify and solve for f yields f = 9.

2. we could have 3 cases given at least one of the two missles hit

m1 hits, m2 misses ==> P1 = (0.1)(0.8)

m1 misses, m2 hits ==> P2 = (0.9)(0.2)

m1 hits, m2 hits ==> P3 = (0.1)(0.2)

only in cases 1 and 3 m1 hits

so probability that missile 1 will hit thetarget given that at least one of the two missiles hit the target

P = P1+P3/(P1+P2+P3) = 0.357

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