
,

,

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

By definition of conditional probability,

For

and

to be independent, we must have

in which case we have

, which is true, so

and

are indeed independent.
Or, to establish independence another way, in terms of conditional probability, we must have

which is also true.
Answer:
The answer would be the third one and the last one trust me
Step-by-step explanation:
I know my MATH mark me brainliest pls
Answer:
Option 2: 1.5 is the correct answer.
Step-by-step explanation:
Given information is:
Mean = μ = $27
SD = σ = $5.50
A z-score simply tells us how far a selected data value from the mean is.
Z-score is denoted by z and is given by the formula:

Let x = $35.25
Putting the values of mean and SD we get,

The value of z-score for a price of $35.25 per barrel is 1.5
Hence,
Option 2: 1.5 is the correct answer.
The system r+l = 46 and 15r + 9l = 396 can be used to determine the number of raspberries boxes and lemon seed boxes sold.
Step-by-step explanation:
Given,
Cost per box of raspberry = $15
Cost per box of lemon seeds = $9
Total boxes sold = 46
Total revenue generated = $396
Let,
r represent the number of raspberries sold
l represent the number of lemon seeds sold
According to given statement;
r+l = 46 Eqn 1
15r + 9l = 396 Eqn 2
The system r+l = 46 and 15r + 9l = 396 can be used to determine the number of raspberries boxes and lemon seed boxes sold.