ANSWER FAST 30 PTS
P(B) = 2/3

P(A ∩ B) = 1/6

What will P(A) have to be for A and B to be independent?

Step-by-step explanation:

ll the answers so far use the addition rule for probability:

P(A∪B)=P(A)+P(B)−P(A∩B)

and then noting that P(A∩B)=P(A)⋅P(B) because A and B are independent. This is a perfectly reasonable approach to obtain the 2/3.

Another way to think about the problem is that P(A∪B) is the probability of either A or B (or both), and this must be equal to one minus the probability that A does not happen and that B does not happen. Symbolically,

P(A∪B)=1−P(A′∩B′).

where A′ and B′ are, respectively, the events “not A” and “not B”. Since A and B are independent, so are A′ and B′, therefore

1−P(A′∩B′)=1−P(A′)⋅P(B′)=1−(1−P(A))⋅(1−P(B))=1−12⋅23=23.

the answer to this question is 23

Step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be