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iVinArrow [24]
3 years ago
14

Six stand up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is dete

rmined by random selection. Find the probability that:
1. Comic D will perform first.
2. Comic B will perform fifth and comic A will perform last.
3. The comedians will perform in the following order: D, B, A, C, F, E
4. Combic F or combic E will perform third.
Mathematics
1 answer:
katrin2010 [14]3 years ago
7 0
<span>Find the probability that 
1.Comic D will perform first

D _ _ _ _ _
 We can fill the 5 blanks with the 5 letters A, B,C,E,F in 5! = 120 ways
The probability of that is 120 ways out of 720 or 120/720 or 1/6. 

2. Comic B will perform fifth and Comic A will perform last
_ _ _ _ B A
We can fill the 4 blanks with the 4 letters C,D,E, F in 4! = 24 ways.
The probability of that is 24 ways out of 720 or 24/720 or 1/30.

3. The comedians will perform in the following order D, B, A, C, F, E
There is just 1 way that can happen. The probability of that is 1 way out of 720 or 1/720.

4.Comic F or E will perform third.
_ _ F _ _ _
There are 5! = 120 ways to fill those 5 blanks with the letters A,B,C,D, E.
In addition to those, there are another 5! = 120 ways to fill these 5 blanks _ _ E _ _ _ with the letters A,B,C,D,F. That's 2(5!) = 2(120) = 240 ways.
The probability of one of those is 240 ways out of 720 or 240/720 or 1/3.
</span>
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Answer: the probability is 0.25

Step-by-step explanation:

We have 10 numbers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Of those, the odd ones are:

1, 3, 5, 7, 9

So we have 5 odd numbers.

The probability that the outcome is an odd number is equal to the number of odd numbers divided the total number of numbers:

p = 5/10 = 0.5

For the second spin the probability is the same, p = 5/10, because the first outcome does not affect the results of the second spin.

The probability of spining an odd number both times, then is the joint probability for two times this same event:

P = (5/10)(5/10) = 0.5*0.5 = 0.25

or 25% in percent form

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3 years ago
Graham recruited student volunteers to participate in his dissertation study. He set up several times for students to come to a
mart [117]

Answer:

Sampling bias

Step-by-step explanation:

Bias refers a prominent problem in statistical analysis whereby one or more analytical factor are favored than the other during an analysis which should be made random. The problem. With Graham's dissertation study is the fact that he failed to randomlyvplace his subjects or observation in the study groups, favoring a particular group with non random subset. When randomization is ejected or missing from an analysis or study, it becomes less and less representative. Here, allotting early Arrivals Into the treatment group has introduced a sampling bias as those who came later, this will also leads to less reproducibility of experiment.

6 0
3 years ago
What is 3/9 in its lowest terms?
Eddi Din [679]
The fraction 3/9 is equivalent to 1/3.The fraction 3/9 is equal to 3÷9 and can also be expressed in decimal form as 0.333333.
5 0
3 years ago
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The number 40 cannot be decomposed into prime factors<br><br>True<br>either<br>False​
dusya [7]

\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}

False, because the number 40 is a composite number, those that cannot be broken down are called Prime Numbers.

Prime numbers are numbers that are used to decompose any number, but prime numbers cannot be decomposed, since they only have two Divisors, which are 1 and itself.

~\sf{Atte: Murdock:)}

3 0
2 years ago
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Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equati
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The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.

Given the table

x         f(x)

-2        -46

-1         -22

0         -10

1           -4

2          -1

We have to choose which statement describes better about function

Let us assume f(x)=ab^x+c

at x=0, f(0)=-10

So, -10 =a+c

Similarly, by satisfying the above table in the f(x)

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f'(x) > 0

So we can say that f(x) is an increasing function.

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g^ \prime (x) = - 18 (\frac{1}{3}  )^ x  ln(1/3)

ln(1/3) < 0

So, g^ \prime (x) > 0

So, g(x) is an increasing function.

For any x∈f(x) and  x∈g(x) g'(x) > f'(x)

So, g increases at a faster average rate

Thus, Both functions are increasing, but function g increases at a faster average rate.

Learn more about increasing functions here: brainly.com/question/12940982

#SPJ10

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