4.1 Experimental And Theoretical Probabilitymr. Mac's Page



Probability

  1. The following table highlights the difference between Experimental Probability and Theoretical Probability. Scroll down the page for more examples and solutions. How To Find The Experimental Probability Of An Event? Step 1: Conduct an experiment and record the number of times the event occurs and the number of times the activity is performed.
  2. New atoms page - Import Cu.inp file from the Cu10k directory Or - Blank Atom page (you must type the crystallographic info) Warning: check the full windows is visible on your PC, smaller screens may cut the lower part.

This file contains notes on theoretical and experimental probability. The page contains the meaning of each type of probability, a number cube, a spinner, data of an experimental, and practice problems. The page asks students to compare the two types of probabilities and encourages a discussion abou.

Probability is a measure of the likelihood that an event will happen.

When dealing with probability, the outcomes of a process are thepossible results. For example, when a die is rolled, the possibleoutcomes are 1, 2, 3, 4, 5, and 6. In mathematicallanguage, an event is a set of outcomes, which describe whatoutcomes correspond to the 'event' happening. For instance, 'rolling aneven number' is an event that corresponds to the set of outcomes{2, 4, 6}.The probability of an event, like rolling an even number, is thenumber of outcomes that constitute the event divided by the totalnumber of possible outcomes. We call the outcomes in an event its'favorable outcomes'.



If a die is rolled once, determine the probability of rolling a4: Rolling a 44.1 experimental and theoretical probabilitymr. mac is an event with 1 favorable outcome (aroll of 4) and the total number of possible outcomes is 6 (a rollof 1, 2, 3, 4, 4.1 Experimental And Theoretical Probabilitymr. Mac

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5, or 6). Thus, the probability of rollinga 4 is .

4.1 Experimental And Theoretical Probabilitymr. Mac's Page Example


If a die is rolled once, determine the probability of rollingat least a 4: Rolling at least 44.1 experimental and theoretical probabilitymr. mac is an event with 3favorable outcomes (a roll of 4, 5

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, or 6) and the total numberof possible outcomes is again 6. Thus, the probability of rolling atleast a 4 is = .

Here are two more examples:
If a coin is flipped twice, determine the probability that it will land heads both times:
Favorable outcomes: 1 -- HH
Possible outcomes: 4 -- HH, HT, TH, TT
Thus, the probability that the coin will land heads both times is .
If Dan grabs one sock from a drawer containing 3 white socks, 4 blue socks, and 5 yellow socks, what is the probability that he will grab a white sock?
Favorable outcomes: 3 (3 white socks)
Possible outcomes: 12 (3 white socks + 4 blue socks + 5 yellow socks)
Thus, the probability that Dan will grab a white sock is = .

Though probabilities are calculated as fractions, they can beconverted to decimals or percents--the Fractions SparkNotein Pre-Algebra explains how to convert fractions to decimalsand the SparkNote on Percents describes how toconvert them to percents.

Boundaries on Probability

4.1 Experimental And Theoretical Probabilitymr. Mac's Page Examples

If all outcomes are favorable for a certain event, its probability is 1. For example, the probability of rolling a 6 or lower on one die is = 1.

If none of the possible outcomes are favorable for a certainevent (a favorable outcome is impossible), the probability is 0.For example, the probability of rolling a 7 on one die is = 0.

b. Joan picks a random counter out of a bag
7 times. What is the experimental
a.
What is the theoretical probability of pickinga yellow counter in simplest form?
Sean is doing an experiment to see how many tails
Trial
1
4
6
Heads
Tails
Tails
b. What is the experimental
(in simplest form)
a. What is the theoretical
How many times would he expect to get the color red
if he did 30 spins?
18 times
60 times
He gets the color red 6 times.
What is the experimental probability of getting blue?
Green
Yellow
Blue
Diana completes an experiment of spinning athree-colored spinner 15 times. She expected to get aprobability of 1/3 for each color, but her numberswere really off. She got 0% probability for red, 60% for green, and 40% for blue.
How could she get her experimental probability closer to her theoretical probability?
She could spin a different spinner.
She needs to spin fewer times.
the theoretical probability is always less than the
experimental probability
the more times the cube is rolled, the closer the
experimental probability gets to the theoretical
probability
the theoretical probability is always greater than
the experimental probability.
Which of the following statements is TRUE?
When rolling a number cube...
Mr. Whatley rolled a fair number cube 50 times. The
number 4 came up 10 times. Calculate the theoretical& experimentalprobabilities of rolling a 4 in simplest form.
Anthony is going to spin the 6-sectioned spinner below to see if he really will get the colorYellow 1/6 of the time.
How many times should he spin the spinner for the outcome of his experiment to best match his theory?
6 spins
1 spin