Chapter 13.4, Problem 14CFU

To determine

To find the probability that none of the $6$ clocks is damaged.

Answer to Problem 14CFU

  $\frac{435643}{560175}$

Explanation of Solution

Given:

The $4$ clocks are damaged out of $100$ grandfather clocks.

Calculation:

Total non-damaged clocks are $100-4=96$

The probability of choosing first non-damaged clock $=\frac{96}{100}$

The probability of choosing second non-damaged clock $=\frac{95}{99}$

The probability of choosing third non-damaged clock $=\frac{94}{98}$

The probability of choosing fourth non-damaged clock $=\frac{93}{97}$

The probability of choosing fifth non-damaged clock $=\frac{92}{96}$

The probability of choosing sixth non-damaged clock $=\frac{91}{95}$

Therefore, the probability that none of the $6$ clocks is damaged

  $=\frac{96}{100}\cdot \frac{95}{99}\cdot \frac{94}{98}\cdot \frac{93}{97}\cdot \frac{92}{96}\cdot \frac{91}{95}=\frac{435643}{560175}$