example

If we roll a standard 6-sided die, describe the sample space and some simple events.

Answer: The sample space is the set of all possible simple events: {1,2,3,4,5,6} Some examples of simple events:

• We roll a 1
• We roll a 5

Some compound events:

• We roll a number bigger than 4
• We roll an even number

 

examples

If we roll a 6-sided die, calculate

1. P(rolling a 1)
2. P(rolling a number bigger than 4)

Answer: Recall that the sample space is {1,2,3,4,5,6}

1. There is one outcome corresponding to “rolling a 1,” so the probability is [latex]\frac{1}{6}[/latex]
2. There are two outcomes bigger than a 4, so the probability is [latex]\frac{2}{6}=\frac{1}{3}[/latex]

Probabilities are essentially fractions, and can be reduced to lower terms like fractions.

This video describes this example and the previous one in detail. https://youtu.be/37P01dt0zsE Let's say you have a bag with 20 cherries, 14 sweet and 6 sour. If you pick a cherry at random, what is the probability that it will be sweet?

Answer: There are 20 possible cherries that could be picked, so the number of possible outcomes is 20. Of these 20 possible outcomes, 14 are favorable (sweet), so the probability that the cherry will be sweet is [latex]\frac{14}{20}=\frac{7}{10}[/latex]. There is one potential complication to this example, however. It must be assumed that the probability of picking any of the cherries is the same as the probability of picking any other. This wouldn't be true if (let us imagine) the sweet cherries are smaller than the sour ones. (The sour cherries would come to hand more readily when you sampled from the bag.) Let us keep in mind, therefore, that when we assess probabilities in terms of the ratio of favorable to all potential cases, we rely heavily on the assumption of equal probability for all outcomes.

example

Compute the probability of randomly drawing one card from a deck and getting an Ace.

Answer: There are 52 cards in the deck and 4 Aces so [latex]P(Ace)=\frac{4}{52}=\frac{1}{13}\approx 0.0769[/latex] We can also think of probabilities as percents: There is a 7.69% chance that a randomly selected card will be an Ace. Notice that the smallest possible probability is 0 – if there are no outcomes that correspond with the event. The largest possible probability is 1 – if all possible outcomes correspond with the event.

This video demonstrates both this example and the previous cherry example on the page. https://youtu.be/EBqj_R3dzd4