Maths a level further probability
Next September I intend to buy a new car. Its registration plate will be of the form
HW 57 MSD
where HW is the local area code for the Isle of Wight, the two digits refer to the year in which the car is registered for the first time, and the last three letters are chosen at random. The five parts of the question refer to the last three letters of the registration plate. You may assume that all 26 letters in the alphabet, of which 5 are vowels and 21 are consonants, are used for each of the random choices.
(i) Find the probability that the random letters on the plate are MSD, appearing in that order. [2]
(ii) Find the probability that the letters are M, S, D in any order. [2]
(iii) Find the probability that just two of the letters are the same. [3]
HW 57 MSD
where HW is the local area code for the Isle of Wight, the two digits refer to the year in which the car is registered for the first time, and the last three letters are chosen at random. The five parts of the question refer to the last three letters of the registration plate. You may assume that all 26 letters in the alphabet, of which 5 are vowels and 21 are consonants, are used for each of the random choices.
(i) Find the probability that the random letters on the plate are MSD, appearing in that order. [2]
(ii) Find the probability that the letters are M, S, D in any order. [2]
(iii) Find the probability that just two of the letters are the same. [3]
Original post by imaan2121
Next September I intend to buy a new car. Its registration plate will be of the form
HW 57 MSD
where HW is the local area code for the Isle of Wight, the two digits refer to the year in which the car is registered for the first time, and the last three letters are chosen at random. The five parts of the question refer to the last three letters of the registration plate. You may assume that all 26 letters in the alphabet, of which 5 are vowels and 21 are consonants, are used for each of the random choices.
(i) Find the probability that the random letters on the plate are MSD, appearing in that order. [2]
(ii) Find the probability that the letters are M, S, D in any order. [2]
(iii) Find the probability that just two of the letters are the same. [3]
HW 57 MSD
where HW is the local area code for the Isle of Wight, the two digits refer to the year in which the car is registered for the first time, and the last three letters are chosen at random. The five parts of the question refer to the last three letters of the registration plate. You may assume that all 26 letters in the alphabet, of which 5 are vowels and 21 are consonants, are used for each of the random choices.
(i) Find the probability that the random letters on the plate are MSD, appearing in that order. [2]
(ii) Find the probability that the letters are M, S, D in any order. [2]
(iii) Find the probability that just two of the letters are the same. [3]
What have you tried?
Think about it in terms of a tree diagram:
(i) 1) either m or not m
2) either s or not s
3) either d or not d
Then just go down the branch of m,s,d
(i) 1) either m or not m
2) either s or not s
3) either d or not d
Then just go down the branch of m,s,d
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