AMS 410 Actuarial Mathematics Fall 2011
Homework 1: General Probability
Due Date: 09/22/2011
1. Given that
P
[
A
∪
B
] = 0
.
7
and
P
[
A
∪
B
] = 0
.
9
, find
P
[
A
]
.
2. Given that
A
and
B
are independent,
P
[
A
] = 2
P
[
B
]
and
P
[
A
∩
B
] = 0
.
15
, find
P
[
A
∩
B
]
.
3. Given that
A
and
B
are independent,
P
[
A
∪
B
] = 0
.
8
and
P
[
B
] = 0
.
3
, find
P
[
A
]
.
4. Given that
P
[
A
] = 0
.
2
, P
[
B
] = 0
.
7
and
P
[
A

B
] = 0
.
15
, find
P
[
A
∩
B
]
.
5.
Assuming
A, B
and
C
are mutually independent, with
P
[
A
] =
P
[
B
] =
P
[
C
] = 0
.
1
,
compute:
(a)
P
[
A
∪
B
]
(b)
P
[
A
∪
B
∪
C
]
.
6. A mattress store sells only king, queen and twinsize mattresses. Sales records at the store
indicate that onefourth as many queensize mattresses are sold as king and twinsize mattresses
combined. Records also indicate that three times as many kingsize mattresses are sold as twinsize
mattresses. Calculate the probability that the next mattress sold is either king or queensize.
7. The probability that a visit to a primary care physicians (PCP) office results in neither lab
work nor referral to a specialist is 35%. Of those coming to a PCP’s office, 30% are referred to
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 Fall '08
 Kerber
 insurance policy, insurance company, policyholders, Room charges

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