M230 Test I Fall 1998 Solutions

1.
(a)

(b) (see part (c))

(c)

(d)
Since

2. 12 out of 100 are dissatisfied, so 88 are satisfied.

S= the set of 4 element subsets of 100 people. n(S) =C(100,4)
E= The event that all 4 chosen were satisfied. n(E) = C(88,4)

3.
(a) where OR

Let D = the event doubles are rolled and T = the event that sum is even (try using "checkerboard" to represent the sample space)
(b)

(c)

4.
(a)

(b)

5.
(a) C(17,4)

(b) C(17,4) - C(13,4) (total # - no MD's) OR C(4,1)C(13,3) + C(4,2)C(13,2) + C(4,3)C(13,1) + C(4,4) (1 MD + 2 MD + 3MD + 4 MD)

(c) C(17,4) - C(14,4) (total - non-pilots)

(d) 11 are neither MD or pilot so C(11,4)

6.

A and B are independent so

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