# Question 81855

##### 2 Answers
Jan 7, 2018

P(divisible by 5)$= \frac{1}{4}$

#### Explanation:

Total no. Of outcomes= 6*4
= 24
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alternate derivation:
There are 4 choice for the first digit;
for each of these there are 3 choices for the second digit;
for each of these there are 2 choices for the third digit;
leaving only 1 possibility for the fourth digit.
Total number of ways of composing a 4-digit number $= 4 \times 3 \times 2 \times 1 = 24$
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Outcomes where divisibility by 5 is possible = 6
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explanation of derivation:
To be divisible by 5 the last digit must be 5;
this leaves 3 choices for the first digit;
2 choices for the second digit; and
1 possibility left for the last digit.
Number of ways of composing 4-digit number ending in 5: $= 3 \times 2 \times 1 = 6$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hence probability of getting a no. which is divisible by 5 = 6/24 = 1/4
Probability =1/4

Jan 7, 2018

The probability is $0.25$. See explanation.

#### Explanation:

The probability can be calculated by dividing the number of outcomes fulfilling the condition by the total number of outcomes:

## $P \left(A\right) = \frac{\overline{\overline{A}}}{\overline{\overline{\Omega}}}$

Here the number of all outcomes can be calculated as:

bar(bar(Omega))=4! =24

The condition for outcomes in $A$ is: the number is divisible by 5, so its last digit has to be $5$ (a number is divisible by $5$ if its units digit is $0$ or $5$, but $0$ is not in the set).
The remaining 3 digits can be arranges in 3! = 6 ways, so:

bar(bar(A))=3! =6

Now we can calculate the probability:

## $P \left(A\right) = \frac{4}{24} = \frac{1}{4} = 0.25$

Original answer:

Probability = Favorable outcome / Total outcome

Outcomes= 1253 1235 1523 1532 1352 1325 2135 2153 2351 2315 2513 2531 3512 3521 3125 3215 3152 3251

Total number of outcomes= 18

Favorable outcomes=1235 1325 2135 2315 3125 3215

Number of favorable outcome= 6

Probability= Favorable outcome / Total outcome

$$              =  6/18#
= 3