Essential Exercise

Lab 3

• Example Problem

• Exercise

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Example Problem

(See example: 20 replicates of a set of five coin tosses)

All of the students (25) in a class each flip a coin in a set of 5 (five times as in this week's exercise) 20 times.  Predict the number of sets (of 5) and the total number that will result in all heads if the following hypothesis is true:  This quarter has 1 head and 1 not head (tail).  The actual class data was:  15 sets out of 2,500.  Compare the actual results with the predicted results.

Answer:

• Coin tosses = 25 X 5 X 20 = 2,500 tosses

• Equation:  Pⁿ
• P is the relative proportion of heads (versus not heads) on a fair coin.  The number of "events" = n
• There are two sides to a coin - 1 head and 1 not head (tail)

• 1 (head)               = 1/2 = 0.5 = P

1 head + 1 not head

• There will be 5 tosses (events) in which each (=5) will be a head.     n = 5
• 0.5⁵ = 0.031 = 3.1% chance that in 5 tosses the coin will come up all heads
• If this is true, the proportion (0.031) can be used to predict how many total (and how many groups of 5) heads will occur:
• Multiply the proportion (0.031) by the total number of future coin tosses (2,500)
• 0.031 X 2,500 = 78 heads
• 78 ¸ 5 = 16 sets of 5 heads.
• 16 sets of 5 out of 2,500 coin tosses will come up heads
• The actual results (15 sets = 15X5 = 75 total heads) were close enough to the predicted (16 sets = 78 total heads).  The hypothesis:  The quarter has one head and one not head was supported.

Exercise

Calculate the predicted answer from this past lab and show your work (i.e. How many sets (of 5) and total will result in all heads - or should have occurred).

How does this compare to the results from this week's simulation?  Provide the same information as the example above and discuss your conclusions.  Explain your answers.  Reminder:

Exercise Answers

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