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stich3 [128]
1 year ago
9

at a particular high school, 42% of the students participate in sports and 25% of the students participate in drama. if 53% of t

he students participate in either sports or drama, what is the probability that a student participates in both sports and drama?
Mathematics
2 answers:
marissa [1.9K]1 year ago
7 0

P( A Student participates in Both sports and Drama) =0.07

<h3>What is the probability?</h3>

The probability of an occurrence can be determined using the probability formula by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

To find the probability that a student participates in both sports and drama:

Let

A =Student  participate in Sport

B = Student  participate in Drama

Thus we have:

P(A) = 0.42

P(B) = 0.25

and

P(Ac and B or A and Bc) =0.53

P(Ac and B ) + P( A and Bc) =0.53

P(B) - P(A and B) + P(A) - P(A and B) = 0.53

0.25 - P(A and B )  +  0.42 - P(A and B) = 0.53

0.25+0.42 - 2 * P( A and B) = 0.53

0.67 - 2 * P(A and B) = 0.53

0.67 - 0.53  = 2* P(A and B)

0.14  =  2 * P(A and B)

0.14 / 2  = P( A and B)

0.07 = P( A and B)

that is:

P( A and B) = 0.07

P( A Student  participate in Both sports and Drama) =0.07.

To learn more about probability, refer to:

brainly.com/question/24756209

#SPJ9

baherus [9]1 year ago
6 0

The probability that a student participates in both sports and drama is 0.14.

<h3>What is the formula for P(AUB), where A and B are any two events?</h3>

If A and B are any two events, then the probability of the joint event (A\cup B) is given by the following formula: P(A\cup B)=P(A)+P(B)-P(A\cap B)

Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.

Suppose S denotes that "a student participates in sports" and D denotes that "a student participates in drama".
So, we have P(S)=\frac{42}{100}=0.42, P(D)=\frac{25}{100}=0.25, P(S\cup D)=\frac{53}{100}=0.53.

We want to find the probability that a student participates in both sports and drama i.e., we want to find P(S\cap D).

By the above formula, we obtain:

P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}

Therefore, the probability that a student participates in both sports and drama is 0.14.

To learn more about probability, refer: brainly.com/question/24756209

#SPJ9

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I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.

Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.

Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.

We want the concentration of antifreeze to be 40% in the new solution, so we need to have

(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4

Solve for <em>x</em> :

0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)

0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24

0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18

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3 years ago
---- PLEASE HELP &lt;3 .. with steps :( &lt;3
Zielflug [23.3K]

1) 6, 18, 54

2) 5/3, 14/9, 41/27

3) 1.5, 2.5, 2.5

Step-by-step explanation:

1)

The function that we have in this problem is

g(x)=3x

We want to find the first 3 iterations.

The initial value is:

x = 2

To find the value of the 1st iteration, we just substitute this value into the expression of the function, and we get:

g_1(x)=3x=3\cdot 2 = 6

The to find the value of the 2nd iteration, we just substitute this value into the expression of the function, and we get:

g_2(x)=3\cdot g_1(x)=3\cdot 6 = 18

Finally, the 3rd iteraction is given by:

g_3(x)=3g_2(x)=3\cdot 18=54

2)

Here in this problem the function that we have to use is

g(x)=\frac{1}{3}x+1

The initial value is

x=2

So the first iteration is given by

g_1(x)=\frac{1}{3}\cdot 2 + 1 = \frac{5}{3}

To find the 2nd iteration, we substitute this value into g(x) again:

g_2(x)=\frac{1}{3}g_1+1=\frac{1}{3}\cdot \frac{5}{3}+1=\frac{5}{9}+1=\frac{14}{9}

Finally, to find the 3rd iteration, we substitute this value into g(x) again:

g_3(x)=\frac{1}{3}\cdot \frac{14}{9}+1=\frac{14}{27}+1=\frac{41}{27}

3)

The function in this problem is

g(x)=-|x-2|+3

The initial value is

x = 0.5

So, the first iteration is:

g_1(x)=-1|0.5-2|+3=-1|-1.5|+3=-1\cdot 1.5 +3=-1.5+3=1.5

The second iteration is given by

g_2(x)=-|g_1-2|+3=-|1.5-2|+3=--0.5+3=2.5

Finally, the 3rd iteration is

g_3(x)=-|g_2-2|+3=-|2.5-2|+3=-0.5+3=2.5

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