rraggio wrote:
A four digit safe code
Permutation
(_)(_)(_)(_)
Note: A safe code can have 0 as the thousands digit; a 4-digit number cannot.
rraggio wrote:
does not contain the digits 1 and 4 at all.
Bag of 8 choices w/ replacement.
rraggio wrote:
What is the probability that it has at least one even digit?
"At least" means Probability Table. Create and work backwards.
****************************
# of evens: Events
0:
1:
2:
3:
4:
----------------------------
Total =
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Total = Fill in Permutation above = 8P4 = (8)(8)(8)(8)
4 evens:
4 evens pick 1 AND
4 evens pick 1 AND
4 evens pick 1 AND
4 evens pick 1 TIMES
the number of ways to arrange EEEE
= 4C1 * 4C1 * 4C1 * 4C1 * 4!/4! = 4*4*4*4 * 1
3 evens:
4 evens pick 1 AND
4 evens pick 1 AND
4 evens pick 1 AND
4 odds pick 1 TIMES
the number of ways to arrange EEEO
= 4C1 * 4C1 * 4C1 * 4C1 * 4!/3!1!= 4*4*4*4 * 4
2 evens:
4 evens pick 1 AND
4 evens pick 1 AND
4 odds pick 1 AND
4 odds pick 1 TIMES
the number of ways to arrange EEOO
= 4C1 * 4C1 * 4C1 * 4C1 * 4!/2!2! = 4*4*4*4 * 6
1 even:
4 evens pick 1 AND
4 odds pick 1 AND
4 odds pick 1 AND
4 odds pick 1 TIMES
the number of ways to arrange EOOO
= 4C1 * 4C1 * 4C1 * 4C1 * 4!/1!3! = 4*4*4*4 * 4
0 evens:
4 odds pick 1 AND
4 odds pick 1 AND
4 odds pick 1 AND
4 odds pick 1 TIMES
the number of ways to arrange OOOO
= 4C1 * 4C1 * 4C1 * 4C1 * 4!/4! = 4*4*4*4 * 1
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# of evens: Events
0: 4*4*4*4*1
1: 4*4*4*4*4
2: 4*4*4*4*6
3: 4*4*4*4*4
4: 4*4*4*4*1
----------------------------
Total = 8*8*8*8 = 4*4*4*4*2*2*2*2 =4*4*4*4*16
****************************
Use the table info to answer any questions.
P(evens = 0) = 1/16
P(evens > 0) = (4+6+4+1)/16
etc.
rraggio wrote:
a) ¼
b) ½
c) ¾
d) 15/16
e) 1/16
ANS: D