What’s the correct answer for this question?

Option B is correct

Step-by-step explanation:

Given the rolling a fair six-sided die once.

The probability of the event A "rolling a 5" is P(A) = 1/6

(There is only a number 5 out of 6 numbers of a die)

The probability of the event B "rolling an odd number" is P(B) = 3/6

(There are 3 odd numbers out of 6 numbers of a die including 1, 3, and 5)

The probability of the event that is "rolling a 5" and "rolling an odd number" is P(A⋂B) = 1/6

(There is only a number satisfying the above event, that is number 5)

If the two events A and B are independent, we will have:

P(A) x P(B) = P(A⋂B)

Now, we check:

(1/6) x (3/6) = (1/6) <=> 1/12 = 1/6 (invalid)

=> A and B are not independent

=> A and B are dependent => Option C and D are incorrect

As the correct formula of conditional probability in case that two events are independent (P(A) = P(A|B) or P(B) = P(B|A)) => Option A is incorrect

=> Only option B is correct

I hope this helps!

false

step-by-step explanation:

i looked it up

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1