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Probability

based on 17 ratings
Author: Cy Ashley Webb

Probability is such an innate part of your life that you rarely think about it. However, every time you use a word like “might,” “may,” “undoubtedly,” “without fail,” or “maybe,” you are voicing a probability that an event will occur.

Scientists and mathematicians like to express probability more accurately. For example, if you toss a penny in the air, the probability (P) that it will land heads can be expressed:

P = # of times it lands heads / total number of coin tosses.

The number will be 5/10, which reduces to ½. This means that you have a 1 out of 2 chance that the penny will land heads.

Life gets more complex when you introduce more possible outcomes. This experiment involves calculating and expressing the possibilities when 3 pennies are tossed simultaneously. Under these circumstances, what are the odds you will get three heads? Three tails? Two heads and a tail? What do you think will happen if you tossed four coins in the air?

Problem:

How does one express the probability of an event and how does probability relate to science?

Materials:

  • Lab book and pencil (all experiments)
  • Four pennies

Procedure:

EXPERIMENT #1

  1. Using a paper and pencil, draw circles with an “H” or a “T” in the center to illustrate the different results when you toss three pennies.
  2. Using the circles that you drew in step 1, express the following:
  • The probability of getting three heads
  • The probability of getting three tails
  • The probability of getting one heads and three tails
  • The probability of getting one tails and three heads.

There are eight distinctly different possibilities so make sure you haven’t left any of them out.

  1. Try tossing three pennies 16 times and writing down the outcomes. Are the probabilities roughly the same as you calculated in step 2? Try tossing three pennies 24 times. Are the probabilities any closer?

EXPERIMENT #2

  1. Repeat Experiment #1, only using four pennies. How many different possibilities are there? Calculate the probability of the following:
  • The probability of getting four heads
  • The probability of getting four tails
  • The probability of getting three heads and one tail
  • The probability of getting three tails and one head
  • The probability of getting two heads and two tails
  • The probability of getting two tails and three heads.

EXPERIMENT #3

  1. Ask each person in your class how tall they are. Write down this information in your lab book. It is important you ask people in the same class because you want data from people who are roughly the same age.
  2. Review your data and note how many people have the same height. For example, in your class there may be 2 people that are 4’1”, 3 people that are 4’1”, 5 people that are 4’5”, 0 people that are 4’6 and 1 person that is 4’7
  3. Graph your data. The x-axis should be number of students and the y-axis should be height. You will probably find that few students are very tall or very short and that the largest number of students falls in the middle. This type of distribution is called a Gaussian curve.
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