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1 answer:
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Answer:
(a)
(b)
(c)
Step-by-step explanation:
Given
i.e. between 4 and 9
Solving (a): Probability that each of the 5 digit are different
Since there is no restriction;
The total possible selection is as follows:
(i.e. any of the 4 start digits)
(i.e. any of the 10 digits 0 - 9)
(i.e. any of the 10 digits 0 - 9)
(i.e. any of the 10 digits 0 - 9)
(i.e. any of the 10 digits 0 - 9)
So, the total is:
For selection that all digits are different, the selection is:
(i.e. any of the 4 start digits)
(i.e. any of the remaining 9)
(i.e. any of the remaining 8)
(i.e. any of the remaining 7)
(i.e. any of the remaining 6)
So:
So, the probability is:
Solving (b): At least 1 repeated digit
The probability calculated in (a) is the all digits are different i.e. P(None)
So, using laws of complement
We have:
So, we have:
Solving (c): An expression to model the probability.
<em>Using (a) as a point of reference, we have;</em>
Where
---- for selection of 5 i.e. n = 5
This can be rewritten as:
4 can be expressed as: 5 - 1
So, we have:
Substitute n for 5
This can be rewritten as:
So, the expression is:
<em>Where n represents the digit number</em>
When two dice are rolled, then possible outcomes are
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Total possible outcomes = 36
In that, we count the ordered pairs that give us sum 5
(1,4) (2,3) (3,2) and (4,1) = 4 outcomes
Probability = (number of times the event occurs)/ (total number of outcomes)
P( sum of 5) = =