Hello I have to construct probability table using 3 coin toss and see how many head I can obtain.I used tree diagram and go the probability and obtain X (number of heads)P(X)01/813/823/831/8 Can you confirm that this is correct?X (number of heads)P(X)X*P(X)(X-m)2*P(X)00.12500.2812510.3750.3750.0937520.3750.750.0937530.1250.3750.28125Totals11.50.75

Question
Asked Nov 13, 2019
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Hello I have to construct probability table using 3 coin toss and see how many head I can obtain.

I used tree diagram and go the probability and obtain 

X (number of heads)

P(X)

0

1/8

1

3/8

2

3/8

3

1/8

 

Can you confirm that this is correct?

X (number of heads)

P(X)

X*P(X)

(X-m)2*P(X)

0

0.125

0

0.28125

1

0.375

0.375

0.09375

2

0.375

0.75

0.09375

3

0.125

0.375

0.28125

Totals

1

1.5

0.75

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Expert Answer

Step 1

It is given that, 3 coins are tossed.

The possible outcomes are {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

The formula for finding probability is shown below:

Number of favorable outcomes
Probability=
Total number of outcomes
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Number of favorable outcomes Probability= Total number of outcomes

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Step 2

In this case, the probability of getting 0 heads is 1/8.

The probability of getting 1 head is 3/8.

The probability of getting 2 heads is 3/8.

The probability of getting 3 heads is 1/8...

X*P(X
(X-m)2*P(X)
(0-1.5)2*0.125=0.28 125
P(X)
0.125 (1/8)
0.375 (3/8) 1*0.375-0.375 (1-1.5)2*0.375-0.09375
0.375 (3/8)
0.125 1/8) 3*0.125-0.375 (3-1.5)2*0.125=0.28125
X
0*0.125-0
0
1
(2-1.5)2*0.375=0.093 75
2*0.375-0.75
2
Totals
0.75
m-1.5
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X*P(X (X-m)2*P(X) (0-1.5)2*0.125=0.28 125 P(X) 0.125 (1/8) 0.375 (3/8) 1*0.375-0.375 (1-1.5)2*0.375-0.09375 0.375 (3/8) 0.125 1/8) 3*0.125-0.375 (3-1.5)2*0.125=0.28125 X 0*0.125-0 0 1 (2-1.5)2*0.375=0.093 75 2*0.375-0.75 2 Totals 0.75 m-1.5

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