Chapter 14.4, Problem 16E

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Chapter
Section

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# APPLICATIONSCombination Lock A safe containing $1 , 000 , 000 is locked with a combination lock. You pay$ 1 for one guess at the six-digit combination. If you open the lock, you get to keep the million dollars. What is your expectation?

To determine

The expected value for the combination lock.

Explanation

Approach:

The compliment of the probability is given as,

p=1p(1)

Here, p is the compliment of the probability and p is the probability.

The expected value is given as,

E=a1p1+a2p2++anpn(2)

Here, a1,a2,,an is the amount of payout and p1,p2,,pn is the probability of payout.

Given:

A safe containing $1,000,000 and for one guess at the six-digit combination you pay$1.

Calculation:

Since there is six digit combination in the lock, then the total possibilities are 1,000,000.

The probability of the safe will open is,

p1=11,000,000

The probability of the safe will not open is,

p2=111,000,000=999,9991,000,000

Calculate the expected value of the game

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