Concept explainers
(a)
To find; the probability of winning when the first digit and randomly guess the others.
(a)
Answer to Problem 61E
The probability of winning if guess the position of given digit is
Explanation of Solution
Given information:
On a game show, given five digits to arrange in the proper order to form the price of a car, If are correct, win a car.
Calculation:
Let us try to find that guess the position of given digit for all five digits position of first digit can be guess in 5 ways.
Position of second digit can be guessed in 4 ways, since the first digit has been guessed and four digits are remaining
Thus, position of third digit can be guessed in 3 ways
Position of fourth digit can be guessed in 2 ways
And position of fifth digit can be guessed in 1 way
The above can be shown as follows
5 | 4 | 3 | 2 | 1 |
Therefore all 5 digits can be arranged in following ways
Since only one way is correct, the probability of winning if guess the position of given digit is
(b)
To find; the probability of winning when randomly guess the position of given digit.
(b)
Answer to Problem 61E
The probability of winning if first digit is known and guess the position of rest of the digits is
Explanation of Solution
Given information:
On a game show, given five digits to arrange in the proper order to form the price of a car, If are correct, win a car.
Calculation:
If the first digit is known, then let us try to find the probability of winning, if the rest of the positions of digits have to be guessed
First digit is known. So,
Position of second digit can be guessed in 4 ways
Thus, position of third digit can be guessed in 3 ways
Position of fourth digit can be guessed in 2 ways
And position of fifth digit can be guessed in 1 way
The above can be shown as follows
0 | 4 | 3 | 2 | 1 |
Therefore all 4 digits can be arranged in following ways
The probability of winning if first digit is known and guess the position of rest of the digits is
Chapter 8 Solutions
Precalculus with Limits: A Graphing Approach
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