Question: At Least 1 Even Number

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In this question, the total no. of possible outcomes is not 10c2, as if two no are selected randomly, these can be the outcomes (23,24,25,26,32,34,35,36,42,43,45,46,52,53,54,56,62,63,64,65), i.e 20 outcomes.However, the final answer will be the same
greenlight-admin's picture

I don't say that the total number of outcomes is 10C2. I say it's 5C2.

We have two options here. We can say that order does not matter in both the numerator and denominator (as I did in my solution). Or we can say that order DOES matter in both the numerator and denominator (as you are suggesting). As you say, however, the answer is the same in both instances.

can we answer it like: Probability of selecting 3 and 5=1/5* 1/4=1/20.

Therefore the ans =1-1/20=18/20.

is it possible?
greenlight-admin's picture

Close! First, 1 - 1/20 does not equal 18/20. So, we have a problem there :-)
Your calculation of (1/5)(1/4) = 1/20 represents the probability of selecting the 3 FIRST and the 5 SECOND.
We must also consider the probability of selecting the 5 FIRST and the 3 SECOND. This too is equal to (1/5)(1/4) = 1/20
So, P(selecting 3 and 5) = 1/20 + 1/20 = 1/10
So, P(selecting at least one even) = 1 - 1/10 = 9/10

Can we solve this problem this way?
We have to select two numbers (Num1 and Num2). There is "and" sign it , It means multiplication. if we select two odd numbers (2/5*1/4)=1/10. Then P(even No:) = 1-1/10=0.9.
Need you Acknowledgment for this procedure.
greenlight-admin's picture

Yes, that's a very valid solution. This practice question appears early in the probability module and is meant to reinforce some of the more basic probability strategies.

Hi,
In your previous video about "p( product of 3 numbers will be odd)", you found out the total no: of outcomes in the denominator by choosing 3 no: from each of the 3 sets, which is 2x5x4, which could be interpreted as 2C1x5C1x4C1.

But why can't I use the same interpretation when it comes to choosing 2 no:s from a SINGLE set to get the denominator as 5C1x4C1 instead of 5C2? although I realize in this case order of the no's are inadvertently taken into consideration, can you give me a sound reasoning as to why that logic/method is forbidden? why am I not allowed to write here 5C1x4C1 while in the former I was able to split into 2C1x5C1x4C1? Is it because in the former it was 3 distinct sets and not allowed for a single set?
greenlight-admin's picture

Your question is similar to the question that Rohan asked at the top of this thread (so my answer will be similar).

We have two options here. We can say that order does not matter in both the numerator and denominator (as I did in my solution). Or we can say that order DOES matter in both the numerator and denominator (as you are suggesting). As you say, however, the answer is the same in both instances.

If you want to say that order matters when calculating the denominator, the we must say that order matters when calculating the numerator.

You have already calculated the denominator (with the premise that order matter), and you got 5C1 x 4C1 = 5 x 4 = 20

Now the denominator. In how many ways can we select 2 of the numbers so that we don't get any even numbers?
There are only 2 odd (i.e., non-even numbers).
So, there are 2 ways (2C1 if you wish) to select the first odd number, and there is 1 way to select the second odd number). So, in TOTAL, the number of ways to select 2 odd numbers = 2 x 1 = 2

So, P(select zero even numbers) = 2/20 = 1/10

So, P(at least 1 even number) =- 1 - 1/10 = 9/10

Why can't you do 2/5C2? Why does the numerator have to be 2C2?
greenlight-admin's picture

Please see my response to ananthu's question above.

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