# Lesson: Mutually Exclusive Events

## Comment on Mutually Exclusive Events

### i don't understand mutually

i don't understand mutually exclusive event in the ball example...please clarify me ### Is there a specific part of

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

### Dear Sir,

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 ### Given: -m = x^2 + 2x - 15

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

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? ### Good catch! I've edited my

Good catch! I've edited my response above.