Your friend decides to flip a coin repeatedly to analyze whether the probability of a head on each flip is 1/2. he flips the coin 10 times and observes a head 7 times. he concludes that the probability of a head for this coin is 7/10=.70.
a. your friend claims that the coin is not balanced, since the probability is not .50. what's wrong with your friend's claim?
b. if the probability of flipping a head is actually 1/2, what would you have to do to ensure that the cumulative proportion of heads falls very close to 1/2?

Step-by-step explanation:

Given that a friend flips a coin 10 times and observes head 7 times.  So he concludes Probability of head =0.1

This is wrong because

i) Just making 10 trials and coming to conclusion is wrong.  Trials should be large to get accurate estimate

ii) The way he threw the coin may be biased so differrent persons should flip and get results for larger trials

iii) External influences such as air, any other disturbance is not considered here.

To avoid all these sampling fluctuations number of trials should be increased with different situations and times.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

step-by-step explanation:

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