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A vehicle license plate in a certain state consists of 2 letters followed by 3 digits, eg. AB211. A license plate is randomly selected from all the possibles ones for this state. Compute the probability of the following events:
(a). No letter or digit is repeated on the license plate selected.
(b). There is at least one vowel on the license plate selected.
(c). The digits are all the same on the license plate selected.
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A vehicle license plate in a certain state consists of 2 letters followed by 3 digits, eg. AB211. A license plate is randomly selected from all the possibles ones for this state. Compute the probability of the following events:
(a). No letter or digit is repeated on the license plate selected. (b). There is at least one vowel on the license plate selected. (c). The digits are all the same on the license plate selected.
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(a) Prob = (26 x 25) x (10 x 9 x 8) / (26 x 26) x (10 x 10 x 10) = 9/13
(b) Prob[at least 1 vowel] = 1 - Prob[no vowel letter at all]
= 1 - [(21 x 21 x 10 x 10 x 10)/(26 x 26 x 10 x 10 x 10)]
= 1 - (21^2)/(26^2)
(c) Prob = (26 x 26) x (10 x 1 x 1)/ (26 x 26) x (10 x 10 x 10)
= 1/100
A vehicle license plate in a certain state consists of 2 letters followed by 3 digits, eg. AB211. A license plate is randomly selected from all the possibles ones for this state. Compute the probability of the following events:
(a). No letter or digit is repeated on the license plate selected. (b). There is at least one vowel on the license plate selected. (c). The digits are all the same on the license plate selected.
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a.) 26*25*10*9*8/26*26*10*10*10 = 9/13
b.) Say there is no vowel 21*21*10*10*10/26*26*10*10*10 = 441/676 Therefore the prob with atleast 1 vowel = 1-441/676
c.) 26*26*10*1*1/26*26*10*10*10 = 1/100
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.