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d1i1m1o1n [39]
2 years ago
5

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

Mathematics
2 answers:
skelet666 [1.2K]2 years ago
8 0

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

The first toss gives two possible outcomes: T or H ( in blue)

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

          S={(H,H),(H,T),(T,H),(T,T)}

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.

Greeley [361]2 years ago
4 0

Answer:

  • 25%

Step-by-step explanation:

<u>We know that:</u>

  • Chances of getting tails on the first try: 50%
  • Chances of getting tails on the second try: 50%

<u>Solution:</u>

  • Chances of getting tails two times in a row: 50% x 50%
  • => Chances of getting tails two times in a row: 50/100 x 50/100
  • => Chances of getting tails two times in a row: 1/2 x 1/2
  • => Chances of getting tails two times in a row: 1/4
  • => Chances of getting tails two times in a row: 25%

Hoped this helped!

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1.20 x 10⁶<br><br>6.0 x 10⁵​
omeli [17]

Answer:

1.20 x 10^{6}=1,200,000\\\\6.0 x 10^{5}=600,000

Step-by-step explanation:

You move the decimal place over 6 times for the first equation and 5 for the second equation.

Hope this helps! Have a great day! :)

8 0
3 years ago
Does anybody know how to solve for “C”?.
Jobisdone [24]

Answer:

c = (b+3a)/2

Step-by-step explanation:

<u>Solve for c:</u>

  • 1/ac = 2/ab - 3/bc

<u>Multiply both sides by abc:</u>

  • abc/ac = 2abc/ab - 3abc/bc
  • b = 2c - 3a
  • b + 3a = 2c
  • 2c = b + 3a
  • c = (b + 3a)/2
8 0
3 years ago
Which of the following is the solution to |x+8|=1?
KonstantinChe [14]

Answer:

-7 OR -9

Step-by-step explanation:

8-7 in the inside

Absolute value of 1 is 1

OR

8-9 in the inside for -1

Absolute value of -1 is 1

Absolute value signs makes everything positive

6 0
3 years ago
Read 2 more answers
Solve the system of equations by substituion,<br> -5x + y = 3<br> 7.5x - 1.5y = 3
Naya [18.7K]
The first equation, make the y as the subject. y = 3 + 5x, then substitute y in the second equation and you will get the value of x. then, substitute the x in the first equation (y = 3 + 5x)
5 0
3 years ago
two sides of a parallelogram meet at an angle of 50 degrees. If the length of one side is 3 meters and the length of the other s
Anon25 [30]

Answer:

The longer diagonal has a length of 7.3 meters.

The angles are 31.65° and 18.35°

Step-by-step explanation:

If one angle of the parallelogram is 50°, another angle is also 50° and the other two angles are the supplement of this angle. so the other three angles are:

50°, 130° and 130°.

The longer diagonal will be the one opposite to the bigger angle (130°), and this diagonal divides the parallelogram in two triangles.

Using the law of cosines in one of these two triangles, we have:

diagonal^2 = a^2 + b^2 - 2ab*cos(130\°)

diagonal^2 = 3^2 + 5^2 - 2*3*5*(-0.6428)

diagonal^2 = 53.284

diagonal = 7.3\ meters

So the longer diagonal has a length of 7.3 meters.

To find the angles that this diagonal forms with the sides, we can use the law of sines:

a / sin(A) = b/sin(B)

5 / sin(A) = diagonal / sin(130)

sin(A) = 5 * sin(130) / 7.3

sin(A) = 0.5247

A = 31.65\°

The other angle is B = 50 - 31.65 = 18.35°

Please check the image attached for better comprehension.

7 0
3 years ago
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