Find the value of x to the nearest thenth<br> A)5.7<br> B)8.2<br> C)4.7<br> D)7

Please helpppp it has to do with P(A U B)

Katyanochek1 [597]

$P(A)=0.5$ , $P(B)=0.6$ , $P(A\cup B)=0.8$

We find the probability of intersection using the inclusion/exclusion principle:

$P(A\cap B)=P(A)+P(B)-P(A\cup B)=0.3$

By definition of conditional probability,

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.3}{0.6}=0.5$

For $A$ and $B$ to be independent, we must have

$P(A\cap B)=P(A)\cdot P(B)$

in which case we have $0.3=0.5\cdot0.6$ , which is true, so $A$ and $B$ are indeed independent.

Or, to establish independence another way, in terms of conditional probability, we must have

$P(A\mid B)\cdot P(B)=P(A)\cdot P(B)\implies P(A\mid B)=P(A)$

which is also true.

7 0

3 years ago

Which expression is equivalent to -51 - (-60)−51−(−60)minus, 51, minus, left parenthesis, minus, 60, right parenthesis?

djyliett [7]

Answer:

it's B.

Step-by-step explanation:

5 0

3 years ago

What is the solution to the compound inequality in interval notation?

ohaa [14]

The given compound inequality is

$2(x+3)>6 \ or \ 2x+3\leq -7$

First we solve the first inequality,

$2(x+3)>6
\\
x+3 >3
\\
x>0$

Now we solve the second inequality

$2x+3\leq -7
\\
2x \leq -7-3
\\
2x\leq -10
\\
x\leq -5$

So we have

$x > 0 \ or \ x\leq -5$

So the required solution is

$( - \infty,-5] \ or \ (0, \infty)$

Correct option is A .

4 0

3 years ago

Can someone help me?

mestny [16]

Answer:

Step-by-step explanation:

To do this, we must use the unit circle. At the angle $\frac{\pi }{6}$ the coordinate pair is ( $\frac{\sqrt{3} }{2}$ , $\frac{1}{2}$ ) and the hypotenuse is 1