Lesson: Mutually Exclusive Events

Rate this video: 
5

Comment on Mutually Exclusive Events

i don't understand mutually exclusive event in the ball example...please clarify me
greenlight-admin's picture

Is there a specific part of that example you don't understand?

Dear Sir,

If x^2 +2x-15 = -m , and x is an integer between -10 and 10 . What is the probability that m is greater than zero ?

I tried to solve this question by solving for the roots but i am having hard time to get the correct answer . Would please help me to solve this one.

Regards
Shubham
greenlight-admin's picture

Given: -m = x^2 + 2x - 15
Factor: -m = (x + 5)(x - 3)

So, there are three ranges of x-values to consider:
1) x < -5
2) -5 < x < 3
3) 3 < x

1) x < -5
When x < -5, (x + 5)(x - 3) is POSITIVE, which means m is NEGATIVE

2) -5 < x < 3
When -5 < x < 3, (x + 5)(x - 3) is NEGATIVE, which means m is POSITIVE

3) 3 < x
When 3 < x, (x + 5)(x - 3) is POSITIVE, which means m is NEGATIVE

So, m is positive only when -5 < x < 3

Since x is an integer, then the possible values of x are: -4, -3, -2, -1, 0, 1 and 2 (7 values)

The question says "x is an integer between -10 and 10 . What is the probability that m is greater than zero ?"

So, there are 19 integers BETWEEN -10 and 10

Of those 19 x-values, 7 of them are such that m evaluates to be positive.

So, P(m is positive) = 7/19

I think, in factorization it should be -m = (x+5) (x-3)

x possible values would be -4 -3 -2 -1 0 1 & 2. isn't it?

but how to tell the probability?
greenlight-admin's picture

Good catch! I've edited my response above.

Add a comment

Have a question about this video?

Post your question in the Comment section below, and we’ll answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching our videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Let us Know

Have a suggestion to make our course even better? Email us today!