Two eventis are independent if knowledge about the first doesn't change your expectation about the second.
a) Independent: After you know that the first die showed 4, you stille expect all 6 numbers from the second. So, the fact that the first die showed 4 doesn't change your expectation about the second die: it can still show numbers from 1 to 6 with probability 1/6 each.
b) Independent: It's just the same as before. After you know that the first coin landed on heads, you still expect the second coin to land on heads or tails with probability 1/2 each. Knowledge about the first coin changed nothing about your expectation about the second coin.
a) Dependent: In this case, there is a cause-effect relation, so the events are dependent: knowing that a person is short-sighted makes you almost sure that he/she will wear glasses. So, knowledge about being short sighted changed your expectation about wearing glasses.
Answer:
0.5
Step-by-step explanation:
Let D be the event of selecting a marble with dots.
Let P be the event of selecting a purple marble.
The probability of selecting a marble with dots, P(D)=0.2
The probability of selecting a marble that is both purple and has dots, 
We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)
By the definition of conditional probability:
The probability of selecting a purple marble given that the marble has dots on it is 0.5.
Answer:
yes
Step-by-step explanation:
You can perform the "line test." If it is a function, there will not be two x's of the same value. In this case, x is 2,6,-1. No number repeats, thus making a function.
The rate of 8 gallons every 25 hours means that the faucet fills 
gallons every hour.
Multiply the unit rate for the number of hours you're interested in to find
Hey there! :)
Answer:
x = -7/12.
Step-by-step explanation:
Given:
Create a common denominator for each term:
Disregard the denominator:
12x + 5 = -2
Subtract 5 from both sides:
12x = -7
Divide both sides by 12:
x = -7/12.
