EXAM P SAMPLE SOLUTIONS
EXAM P SAMPLE SOLUTIONS
EXAM P SAMPLE SOLUTIONS
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4. Solution: A<br />
For i = 1, 2, let<br />
Ri= event that a red ball is drawn form urn i<br />
Bi= event that a blue ball is drawn from urn i .<br />
Then if x is the number of blue balls in urn 2,<br />
0.44 = Pr[ R IR U B IB ] = Pr[ R IR ] + Pr B IB<br />
= Pr[ R1] Pr[ R2] + Pr[ B1] Pr[<br />
B2]<br />
4 ⎛ 16 ⎞ 6 ⎛ x ⎞<br />
= ⎜ ⎟+ ⎜ ⎟<br />
10 ⎝ x+ 16 ⎠ 10 ⎝ x+<br />
16 ⎠<br />
Therefore,<br />
32 3x 3x+ 32<br />
2.2 = + =<br />
x+ 16 x+ 16 x+<br />
16<br />
2.2x+ 35.2 = 3x+ 32<br />
0.8x = 3.2<br />
x = 4<br />
( ) ( ) [ ]<br />
1 2 1 2 1 2 1 2<br />
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5. Solution: D<br />
Let N(C) denote the number of policyholders in classification C . Then<br />
N(Young ∩ Female ∩ Single) = N(Young ∩ Female) – N(Young ∩ Female ∩ Married)<br />
= N(Young) – N(Young ∩ Male) – [N(Young ∩ Married) – N(Young ∩ Married ∩<br />
Male)] = 3000 – 1320 – (1400 – 600) = 880 .<br />
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6. Solution: B<br />
Let<br />
H = event that a death is due to heart disease<br />
F = event that at least one parent suffered from heart disease<br />
Then based on the medical records,<br />
c 210 −102<br />
108<br />
P⎡ ⎣H ∩ F ⎤<br />
⎦ = =<br />
937 937<br />
c 937 − 312 625<br />
P⎡ ⎣F ⎤<br />
⎦ = =<br />
937 937<br />
c<br />
P⎡H ∩ F ⎤<br />
c<br />
108 625 108<br />
and P⎡H | F<br />
⎣ ⎦<br />
⎣<br />
⎤<br />
⎦ = = = = 0.173<br />
c<br />
P⎡ ⎣F ⎤<br />
⎦<br />
937 937 625<br />
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