Represent and Determine Probability Question
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Grade 11 Represent and Determine Probability CCSS: HSS-CP.B.9
At Karen's school, each locker comes with a lock that already has a combination. The locks use four numbers between 1 and 60 which aren't repeated. Karen is hoping that her locker combination has the numbers 4, 10, 22, and 50 which happen to have special significance for her. She doesn't care what order these numbers are in. She determines that there are P(60,4) total possibilities for the locker combination, and P(4,4) possibilities that include her numbers. Therefore, the probability that she gets her numbers is 2.1×10-6. Is she correct, and if not, why?
- No. Although justified in using permutations for the total number of possibilities, since order does matter, she should have used combinations to calculate the number of possibilities which include her numbers, since she doesn't care about the order for them. The probability should be C(4,4)P(60,4)=8.5×10-8.
- No. Even though the end answer is correct, it is by chance. The total possibilities for locker combinations is C(60,4) and the number of possibilities that include her numbers is C(4,4). This just happens to also equal 2.1×10-6.
- No. The correct number of possibilities for the lock combination should be 604. Therefore, the probability would be P(4,4)604=1.9×10-6.
- Yes. Karen's method is correct.