Difference between revisions of "2005 iTest Problems/Problem 13"
(Created page with "==Problem== In a moment of impaired thought, Joe decides he wants to dress up as a member of NSYNC for his school Halloween party that night. If he dresses up as JC Chasez, he...") |
(→See Also) |
||
| Line 5: | Line 5: | ||
==See Also== | ==See Also== | ||
| − | {{iTest box|year=2005|num-b= | + | {{iTest box|year=2005|num-b=12|num-a=14}} |
[[Category: Introductory Combinatorics Problems]] | [[Category: Introductory Combinatorics Problems]] | ||
Latest revision as of 19:31, 13 October 2025
Problem
In a moment of impaired thought, Joe decides he wants to dress up as a member of NSYNC for his school Halloween party that night. If he dresses up as JC Chasez, he has a probability of 
of getting beat up at the party. If he dresses up as Justin Timberlake, he has a 
probability of getting beat up at the party. If he dresses up as any other member of NSYNC, he won’t get beat up because no one will recognize his costume. If there is an equal probability of him dressing up as any of the 
NSYNC members, what is the probability he will get beat up at the Halloween party?
Solution 1
We can use casework and add up the probability of each individual case. Joe dresses as JC Chasez with probability 
, and has probability of getting beat up in this costume as . The overall probability contribution here is 
. Similarly for dressing as Justin Timberlake, his probability to get beat up here is 
. Since there is no chance of him getting beaten up if he dresses as one of the other members, we can simply add 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 12 |
Followed by: Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
