Answer:
a) 1/64
b) 1/4096
Step-by-step explanation:
As you can tell from the example, the exponent of 1/2 is the number of heads in a row.
a) p(6 heads in a row) = (1/2)^6 = 1/(2^6) = 1/64
b) p(12 heads in a row) = (1/2)^12 = 1/(2^12) = 1/4096
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<em>Additional comment</em>
The probability of a head is 1/2 because we generally are concerned with a "fair coin." That is defined as a coin in which each of the 2 possible outcomes has the same probability, 1/2. Similarly, a "fair number cube" has 6 faces, and the probability of each is defined to be the same as any other, 1/6. Loaded dice and unfair coins do sometimes show up in probability problems.
Answer:
Number 4 is neither, number 6 is perpendicular
Step-by-step explanation:
<h3>
Answer: 9</h3>
======================================================
Explanation:
You're on the right track. The 15 C 9 refers to the nCr combination formula which is built into the binomial probability.
The 0.75^9 is also correct
The 0.15^(15-7) portion is not correct. That 0.15 should be 0.25 so it adds to 0.75 to get 1.00 or just 1
Also, the (15-7) portion should be (15-9)
-----------------------------------
So here's how the steps should look
B(x) = probability of getting a certain x value in a binomial distribution
B(x) = (nCx)*(p)^(x)*(1-p)^(n-x)
B(9) = (15C9)*(0.75)^(9)*(1-0.75)^(15-9)
B(9) = 5005*(0.75)^(9)*(0.25)^(6)
B(9) = 0.09174776729197
B(9) = 0.0917
The probability of getting exactly 9 flights on time is roughly 0.0917
This applies to one trial.
In 100 trials, we expect about 100*0.0917 = 9.17 = 9 flights to be on time.
It's a coincidence that we get a final answer of 9 which matches with the other 9 mentioned in the instructions. This won't always be the case.
Option A
The solution set of the equation is {-12, -2}
<h3><u>Solution:</u></h3>
Given equation is:
We have to find the solution set of this equation by completing the square
First, rearrange the equation so that only zero will be on the right side:
----- eqn 1
<em><u>The general form of quadratic equation is:</u></em>
where 
On comparing the given eqn 1 with general quadratic equation, we get
a = 1
b = 14
c = 24
In completing the square, we take half of coefficient of middle term "x" and then square it. Then we add it on both sides of the equation
So to complete the square, add 
to both sides of the equation
Take square root on both sides
Now make two equations
x + 7 = + 5 and x + 7 = -5
x = +5 - 7 = -2
x = -2
And,
x + 7 = -5
x = -5 - 7 = -12
x = -12
Therefore, the solution set of the equation is {-12, -2} and option A is correct
