?Ten slips of paper are each marked with a different number (from 0 to 9) and placed in a basket. A slip is pulled out, its number is recored (in the order it is drawn), and the slip is replaced. This is done 4 times.
How to find the probabilities that the follow (numbers) are formed?
a) 1234
b) a number which starts with 5
c) a number with no repetition of digits.
d) a number that does not contain 2,3, or 4
How to find the probabilities that the follow (numbers) are formed?
a) 1234
b) a number which starts with 5
c) a number with no repetition of digits.
d) a number that does not contain 2,3, or 4
2 Answers
As explained below.
Explanation:
There are
a) To form the number
The numbers must be drawn in this order.
The total number of ways of drawing
b) To form a number which start with
However, the numbers which follow can be any of the
This can also be calculated as
c) If no repetition is allowed, then the number of choices drops with each successive draw.
There are
Number of ways
(This allows for the first digit to be
If the first digit may not be
then the number of ways
d) If a number may not contain
Number of ways is
If the first digit may be
If the first digit may not be
the number of ways
Explanation:
a.
Therefore,
b.
c. With one card:
With two cards:
Explanation: with one card, it is impossible to repeat numbers, so
With three cards:
With four cards:
d.