Which equation implies that a and b are independent events?

p(a b) = p(a)

p(b)

p(a) = p(b)
p(b|a) = p(a)
p(a b) = p(a) p (b)
p(a|b) = p(b|a)

Independent events are events that are non-mutually exclusive which means that the probability of getting event A true is not dependent on the occurence of event B or vice versa. The equation that implies this relationship is C. P(A B) = P(A) P (B)

 First option is correct.

Step-by-step explanation:

Since we have given that A and B are two events then,

According to "Probability rule":

But we have also given that event A and B are two independent events .

independent events are those events if occurrence of one has no effect on the other.

so,

Hence, First option is correct.

Year 2,590

Step-by-step explanation:

In this question, we are asked to calculate the year at which the population of a country will be a certain amount given the exponential equation through which the equation proceeds.

Let’s rewrite the exponential function;

A = 429e^0.024t

Now here, our A is 559,000,000

t is unknown

Let’s substitute this value of A in the exponential equation;

559,000,000 = 429 * e^0.024t

559,000,000/429 = e^0.024t

1,303,030.303030303 = e^0.024t

Let’s take the logarithm of both sides to base e, we have;

ln(1,303,030.303030303) = ln(e^0.024t)

14.08 = 0.024t

t = 14.08/0.024

t = 587 years

Now, we add this to year 2003 and this gives year 2590