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bagirrra123 [75]
3 years ago
8

10 POINTS AND BRAINLIEST URGENT MATH QUESTION SEE PICTURE

Mathematics
1 answer:
Lostsunrise [7]3 years ago
5 0

The point-slope form:

y-y_1=m(x-x_1)

m - slope

(x_1,\ y_1) - point

We have the point (3,\ -2)\to x_1=3,\ y_1=-2 and the slope m=\dfrac{2}{3}

Substitute:

y-(-2)=\dfrac{2}{3}(x-3)\\\\\boxed{y+2=\dfrac{2}{3}(x-3)}

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A coin is tossed twice. What is the probability of getting a tail in the first toss and a tail in the second toss?
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Answer:

<h2>1/4 Chances</h2><h2>25% Chances</h2><h2>0.25 Chances (out of 1)</h2>

Step-by-step explanation:

Two methods to answer the question.

Here are presented to show the advantage in using the product rule given above.

<h2>Method 1:Using the sample space</h2>

The sample space S of the experiment of tossing a coin twice is given by the tree diagram shown below

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The second toss gives two possible outcomes: T or H (in red)

From the three diagrams, we can deduce the sample space S set as follows

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with n(S)=4 where n(S) is the number of elements in the set S

tree diagram in tossing a coin twice

The event E : " tossing a coin twice and getting two tails " as a set is given by

          E={(T,T)}

with n(E)=1 where n(E) is the number of elements in the set E

Use the classical probability formula to find P(E) as:

          P(E)=n(E)n(S)=14

<h2>Method 2: Use the product rule of two independent event</h2>

Event E " tossing a coin twice and getting a tail in each toss " may be considered as two events

Event A " toss a coin once and get a tail " and event B "toss the coin a second time and get a tail "

with the probabilities of each event A and B given by

          P(A)=12 and P(B)=12

Event E occurring may now be considered as events A and B occurring. Events A and B are independent and therefore the product rule may be used as follows

        P(E)=P(A and B)=P(A∩B)=P(A)⋅P(B)=12⋅12=14

NOTE If you toss a coin a large number of times, the sample space will have a large number of elements and therefore method 2 is much more practical to use than method 1 where you have a large number of outcomes.

We now present more examples and questions on how the product rule of independent events is used to solve probability questions.

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Answer:

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Step-by-step explanation:

We are given the following in the question:

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