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Assume that for each of the following statements, the information provided is all that is known about a coin that was flipped 20 times. Which statement gives the strongest evidence that the coin is NOT fair?

A. It landed on tails the first 9 times it was flipped.
B. It landed on tails the first 17 times it was flipped.
C. It landed on tails the first 10 times it was flipped.
D. It landed on heads 12 times and tails 8 times.
E. It landed on heads 10 times and tails 10 times.

Sagot :

GinnyAnswer
Let's determine which statement provides the strongest evidence that the coin is not fair by evaluating the deviation from what is expected in a fair coin flip. For a fair coin, we expect about 10 heads and 10 tails in 20 flips.

Here are the given scenarios and their evaluations:

A. The coin landed on tails the first 9 times it was flipped.
- Out of 20 flips, there are 9 tails.
- The deviation from the expected 10 tails is [tex]\(|10 - 9| = 1\)[/tex].

B. The coin landed on tails the first 17 times it was flipped.
- Out of 20 flips, there are 17 tails.
- The deviation from the expected 10 tails is [tex]\(|10 - 17| = 7\)[/tex].

C. The coin landed on tails the first 10 times it was flipped.
- Out of 20 flips, there are 10 tails.
- The deviation from the expected 10 tails is [tex]\( |10 - 10| = 0 \)[/tex].

D. The coin landed on heads 12 times and tails 8 times.
- Out of 20 flips, there are 8 tails.
- The deviation from the expected 10 tails is [tex]\( |10 - 8| = 2 \)[/tex].

E. The coin landed on heads 10 times and tails 10 times.
- Out of 20 flips, there are 10 tails.
- The deviation from the expected 10 tails is [tex]\(|10 - 10| = 0\)[/tex].

The deviation values for each scenario are:
- A: 1
- B: 7
- C: 0
- D: 2
- E: 0

The highest deviation from the expected 10 tails is 7 tails, which occurs in scenario B.

So, option B, where the coin landed on tails the first 17 times it was flipped, gives the strongest evidence that the coin is not fair.
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