Question

Suppose you toss a fair coin 10,000 times. Should you expect to get exactly 5000 heads? Why or why not? What does the law of large numbers tell you about the results you are likely to get? Choose the correct answer below.

1)Should you expect to get exactly 5000 heads? Why or why not?

A)You shouldn't expect to get exactly 5000 heads, because you cannot predict precisely how many heads will occur.

B.You shouldn't expect to get exactly 5000 heads, because it is not easy to count precisely the number of heads that occurred.

C.You should expect to get exactly 5000 heads, because for a fair coin, the proportion of heads is exactly 50%.

D.You should expect to get exactly 5000 heads, because the proportion of heads should be 50% for such a large number of tosses.

2) What does the law of large numbers tell you about the results you are likely to get?

A. The proportion of heads should approach 0.5 as the number of tosses decreases.

B.The proportion of heads should approach 0.5 as the number of tosses approaches an exact number.

C.The proportion of heads should not approach 0.5 as the number of tosses increases.

D.The proportion of heads should approach 0.5 as the number of tosses increases.

Answer #1

(1)

Correct option:

**(A) You shouldn't expect to get exactly 5000 heads,
because you cannot predict precisely how many heads will
occur.**

Explanation: It is not possible to exactly calculate population parameter from sample statistic.We can only make estimate the parameter.

(2)

Correct option:

**(D) The proportion of heads should approach 0.5 as the
number of tosses increases.**

Explanation:By law of large numbers, as the sample size increases the sample statistics will approach population parameter.

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