1. A group of students has devised a code made of four characters: 1st character
ID: 3709393 • Letter: 1
Question
1. A group of students has devised a code made of four characters: 1st character is a hexadecimal digit (0-F) 2nd character is a letter that represents color (one of) . R-red O orange Y-yellow . G-green B-blue indigo V violet 3rd character is H or T (Heads or Tails from flip of coin) 4th character is 1-6 (roll of die) Write down any 5 valid codes If S is the sample space, calculate IS| For the event, where the first characters is "A", and the color is green, list the elementary events of the event, and give the size of the event set Assume that all outcomes of experiment are equally likely. Find the probability of the event in step c a) b) c) d)Explanation / Answer
1st character is a hexa decimal digit (0-F)
2nd character is one of [R O Y G B I V]
3rd character is [H T]
4th character is [1 2 3 4 5 6]
a.
5 valid codes could be
1. 1 R H 1
2. 2 O T 3
3. 9 G T 5
4. A Y H 4
5. C B T 6
b.
Total size of sample space is
16*7*2*6
|S| = 1344
c.
Give first character is 'A' and color is 'Green'
We are left with 2 choices (H,T) and (1 to 6)
So, there are total 6*2 = 12 elementary events
they are
A G H 1
A G H 2
A G H 3
A G H 4
A G H 5
A G H 6
A G T 1
A G T 2
A G T 3
A G T 4
A G T 5
A G T 6
Size of event set is 12
d. There are 12 events in event set. Probability of occurance of an event is 1/12
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