The probability that a student passes mathematics class is 0.85, the probability that he passes history class is 0.70, and the probability that he passes mathematics and history is 0.50. are the two events independent of each other?

No

Step-by-step explanation:

To determine if two events are independent, we use the multiplication rule which states P (A and B) = P(A) * P(B).

Here P(math) = 0.85 and P(history) = 0.70. The P(math and history) = 0.50. Multiply the probabilities and see if it is the same as 0.50.

0.85*0.70 = 0.595

It is not the same so these are not independent.

{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

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step-by-step explanation: