Difference between revisions of "2005 iTest Problems/Problem 10"
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| + | ==Problem== | ||
| + | The probability of U2 dismantling an atomic bomb is <math>11\%</math>. The probability of Coldplay finding X & Y is <math>23\%</math>. If the probability of both events occurring is <math> 6\%,</math> find the probability that neither occurs. | ||
| + | ==Solution 1== | ||
| + | By the Principle of Inclusion-Exclusion, the probability of U2 dismantling an atomic bomb and Coldplay NOT finding X & Y is <math>11\%-6\%=5\%</math>. Similarly, the probability of Coldplay finding X & Y and U2 NOT dismantling an atomic bomb is <math>17\%</math>. Therefore, the probability that neither occurs is <math>100\%-5\%-17\%-6\%=\boxed{72\%}</math>. | ||
| + | ==See Also== | ||
| + | {{iTest box|year=2005|num-b=9|num-a=11}} | ||
| + | |||
| + | [[Category: Introductory Combinatorics Problems]] | ||
Latest revision as of 19:02, 13 October 2025
Problem
The probability of U2 dismantling an atomic bomb is 
. The probability of Coldplay finding X & Y is 
. If the probability of both events occurring is 
find the probability that neither occurs.
Solution 1
By the Principle of Inclusion-Exclusion, the probability of U2 dismantling an atomic bomb and Coldplay NOT finding X & Y is 
. Similarly, the probability of Coldplay finding X & Y and U2 NOT dismantling an atomic bomb is 
. Therefore, the probability that neither occurs is 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 9 |
Followed by: Problem 11 | |
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