+173 Given that a and b are real numbers such that -3 ≤ a ≤ 1 and -2 ≤ b ≤ 4, and values for a and b are chosen at random, what is the probability that product a * B is positive?
+983 Alright, here we go:
For two number's product to be positive, those numbers must be both positive or both negative, but cannot be zero.
This is because zero is neither positive nor negative, and 0 * n = 0.
The first step is to find the total number of combination: (a,b).
This can be done by:
\((1-(-3)+1)\cdot(4-(-2)+1) =5\cdot7=35.\)
There are a total of 35 different combinations.
Out of those combinations there are:
( -3 , -2 ) ; ( -3 , -1 ) ; ( -2 , -2 ) ; ( -2 , -1 ) ; ( -1 , -2 ) ; ( -1 , -1 )
( 1 , 1 ) ; ( 1 , 2 ) ; ( 1 , 3 ) ; ( 1 , 4 )
10 that work.
The probabilty of this happening is:
\(\boxed{\frac{10}{35}=\frac{2}{7}}\)
I hope this helped,
Gavin.
+983 Alright, here we go:
For two number's product to be positive, those numbers must be both positive or both negative, but cannot be zero.
This is because zero is neither positive nor negative, and 0 * n = 0.
The first step is to find the total number of combination: (a,b).
This can be done by:
\((1-(-3)+1)\cdot(4-(-2)+1) =5\cdot7=35.\)
There are a total of 35 different combinations.
Out of those combinations there are:
( -3 , -2 ) ; ( -3 , -1 ) ; ( -2 , -2 ) ; ( -2 , -1 ) ; ( -1 , -2 ) ; ( -1 , -1 )
( 1 , 1 ) ; ( 1 , 2 ) ; ( 1 , 3 ) ; ( 1 , 4 )
10 that work.
The probabilty of this happening is:
\(\boxed{\frac{10}{35}=\frac{2}{7}}\)
I hope this helped,
Gavin.
