Question

Every day we all make many decisions. Sometimes they are small, like how long will it take be to get to the grocery store; would I like to see a particular movie or go to a particular restaurant. Think of three decision you have made recently. You do not need to give the details of the decision but answer the following questions. Of the three, did you have "complete" knowledge beforehand of the outcome? If you did not, what was your decision based on?

You are watching a baseball game with your friends. The batter-up has an average of 333, meaning he gets a hit one out of three times at bat. However in his last 12 at bats he has not gotten a hit. Your friend says that this time at bat he is more likely to get a hit because based on his average his is due. What do you think?

Also, you are flipping a coin 20 times in a row. You have flipped it 4 times and this is the results: H, H, H, H. You know that the long term probability of a coin toss is 50/50. Is the probability that the next coin toss (#5) effected by the fact that the last four tosses all came up Heads?

Discuss (4-5 sentences minimum) these two questions.Do not copy and paste from internet sources.

5 to 6 complete sentences. Do not copy and paste from internet sources.

Answer 1

Conclusions arrived at on both the above occasions are incorrect because of the following reason.

In case of first occasion: Batting average = 0.333 = 1/3 = 1 success in 3 trials is true only for large samples by Law of Large Numbers. Here since the sample size = n = 12< 30, Small Sample. So, Law of Large Numbers is not applicable. So, the conclusion that this time at bat he is more likely to get a hit because based on his average his is due is incorrect.

In case of second occasion: probability of a coin toss is 50/50 is true only for large samples by Law of Large Numbers. Here since the sample size = n = 4 < 30, Small Sample. So, Law of Large Numbers is not applicable. So, the probability that the next coin toss (#5) is not effected by the fact that the last four tosses all came up Heads.