Answer:
P (X ≤ 4)
Step-by-step explanation:
The binomial probability formula can be used to find the probability of a binomial experiment for a specific number of successes. It <em>does not</em> find the probability for a <em>range</em> of successes, as in this case.
The <em>range</em> "x≤4" means x = 0 <em>or</em> x = 1 <em>or </em>x = 2 <em>or</em> x = 3 <em>or</em> x = 4, so there are five different probability calculations to do.
To to find the total probability, we use the addition rule that states that the probabilities of different events can be added to find the probability for the entire set of events only if the events are <em>Mutually Exclusive</em>. The outcomes of a binomial experiment are mutually exclusive for any value of x between zero and n, as long as n and p don't change, so we're allowed to add the five calculated probabilities together to find the total probability.
The probability that x ≤ 4 can be written as P (X ≤ 4) or as P (X = 0 or X = 1 or X = 2 or X = 3 or X = 4) which means (because of the addition rule) that P(x ≤ 4) = P(x = 0) + P(x = 1) + P (x = 2) + P (x = 3) + P (x = 4)
Therefore, the probability of x<4 successes is P (X ≤ 4)
If an experiment has 
possible outputs, each with probability
then the sum of all probabilities is always one:
So, in your case, you have
plugging in the given values:
we can deduce that
Answer:
(D) Volcanic Gray
Step-by-step explanation:
The ratio of Volcanic Gray is 8:1 (8 gallons of black to 1 gallon of white). If you double this ratio it is now 16:2 (16 gallons of black to 2 gallons of white). Thus your answer is D.
Subtract y from the fist equation to get an expression for x.
... x + y - y = 6 - y
... x = 6 - y
Assuming your multiplication symbol (×) in the second equation is supposed to be the variable x, performing the substitution gives
... 3(6-y) - y = 6 . . . . . . equation after substitution
... 18 - 4y = 6 . . . . . . . . eliminate parentheses
... 12 - 4y = 0 . . . . . . . . subtract 6
... 3 - y = 0 . . . . . . . . . . divide by 4
... 3 = y . . . . . . . . . . . . .add y
Now, we can use the above expression for x to find x
... x = 6 - y = 6 - 3
... x = 3
The solution of the system of equations is (x, y) = (3, 3).
