What are two ways to determine the probability that two independent events, A and B, will occur together.

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.

Some other examples of independent events are:

The events A and B are independent if any one of the following three equivalent conditions hold:

P(A ∩ B) = P(A)P(B)

P(A|B) = P(A)  B has no effect on A

P(B|A) = P(B)  A has no effect on B

Intuitively, two events are independent if the occurrence of one has no effect at all on the probability of the other.

To find the probability of two independent events that occur in sequence, find the probability of each event occurring separately, and then multiply the probabilities.

Multiplication Rule: When two events, A and B, are independent, the probability of both occurring is:

P(A and B) = P(A) · P(B)

To test whether two events A and B are independent, calculate P(A), P(B), and P(A ∩ B), and then check whether P(A ∩ B) equals P(A)P(B). If they are equal, A and B are independent; if not, they are dependent.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.