Need Help: Counting methods & Probability questions

[harmeet]

The questions are -

1. You are taking a test that has 10 questions, and the answer to each question will either be "all", "some", or "none." If you leave none blank, in how many ways can you answer the questions?

a. 3000
b. 19,683
c. 59,049
d. 30


2. A person can purchase a $50,000 flight insurance policy for an international flight at a cost of $50. Past history indicates that the probability of a person dying on an international flight with this particular airline is 0.0012. Determine the insurance company's expected gain per policy.
[Hint]

a. $29.88
b. $19.98
c. $39.94
d. $49.94

I'd really appreciate the solutions to these questions. I have just started preparing for GMAT & figured out Probability is my weak area.

Thanks
Harmeet.

[kstv]

1) The probability of answering a question is 3ways.
So answering 10 Qs is 3^10
This is a big no.
but 3 ¹ = 3 3²= 9 3³= 27 3^4 = 81 the last digit repeat inthe order 1,9,7 and 1
This tech. helps us to choose the right oprtion.
IMO C

[kstv]

Out of the $50 the amount they have to set aside for payment in event of an accident = 50*.0012 = 0.06
Their gain per policy is = 50-0.06 = $ 49.94

I am trying to tackle this problem in a diff way.
If the probability of an accident is .0012 it means there will be 12 accident in 10,000 flights
So in 10,000 flights the company has keep reserve to pay 12 X $ 50000 or 12*5*10,000
In 10, 000 flights the income through premium is $50 X 10000 or $5*10*10,000
Here there is a loss, why ?

[nagaraja83]

the loss u see is because u made an inherent assumption that 1 person per flight is buying the insurance. In that case it is a loss

[ajith]

The questions are -

1. You are taking a test that has 10 questions, and the answer to each question will either be "all", "some", or "none." If you leave none blank, in how many ways can you answer the questions?

a. 3000
b. 19,683
c. 59,049
d. 30

There are three ways to answer each of the question. Total no of ways = 3*3*...*3 (10 times) = 3^10 = 59049 (3^10 has to end with a 9)


2. A person can purchase a $50,000 flight insurance policy for an international flight at a cost of $50. Past history indicates that the probability of a person dying on an international flight with this particular airline is 0.0012. Determine the insurance company's expected gain per policy.
[Hint]

a. $29.88
b. $19.98
c. $39.94
d. $49.94

Expected cost = Expected probability of a person dying on an international flight* Cover offered
=0.0012* 50000
=60 dollars

In which case the insurance company will suffer a loss of 10 dollars per policy which is nonsensical
[but If we take 0.0012 is a percentage figure in which case the cost becomes 0.6 dollars and the gain is 49.4]

Find my answers inline