<p>Hello guys ,
can you help me with this question please.
A number "a" is to be chosen at random from the set ( 1,2,3,4,5,6). A number "b" is then to be chosen at random from the remaing five numbers . What is the probability that a÷b will be an integer .
The answer is 4÷15 , why :) </p>
<p>I’m not usually an advocate of listing out all the possible cases, but for this problem, it is probably the best solution. </p>
<p>There are 6*5 = 30 possibilities for (a,b), each equally likely. We do casework on b:</p>
<p>b = 1 --> (2,1), (3,1), …, (6,1) (5 possibilities)
b = 2 --> (4,2), (6,2) (2 possibilities)
b = 3 --> (6,3) (1 possibility)
b = 4, 5, or 6 --> no solutions since a != b and a <= 6</p>
<p>The probability is (5+2+1)/30 = 4/15.</p>
<p>If “a” got to be 6, then there are three probabilities that “b” gets to be a number divsible by 6. (3,2,1)
If “a” got to be 5, then there is only one probability that “b” could be a number divisible by 5. (1)
If “a” got to be 4, then there are 2 probabilities that “b” could be divisible by 4. (either 2 or 1)
If “a” got to be 3, then there’s only one probability that “b” could be divisible by 3. (1)
If “a” got to be 2, then there’s only one probability that “b” could be divisible by 2. (1)
If “a” got to be 1, then there are no probabilities that “b” would be divisible by 1.</p>
<p>Count the number of probabilities of having an integer. 6 has 3… 5 has 1… 4 has 2… 3 has 1… 2 has 1 and 1 has none. So you have 8 probabilities that a/b would be an integer.</p>
<p>The probabilities of a/b altogether are 30. (if a is 6, b could be 1,2,3,4, or 5 … and so on for each number)</p>
<p>8/30 = 4/15.</p>
<p>Thanx alot 
</p>