This is for your practice!
The first data story in this worksheet is an inquiry into the breakfast-eating habits of college students.
A group of 460 college students was surveyed over several typical weekdays, and 253 of them reported that they had eaten breakfast that day. Let B be the event of interest-that a college student eats breakfast.
Based on this information, what is the estimate of P(B), the probability that a randomly chosen college student eats breakfast?
What would you write as an answer? Practice, write it out, and discuss. Then, submit your answer on Canvas.
Which of the following would provide even more convincing evidence that, indeed, P(B) is roughly 0.55?
As you think about the correct answer, suppose I selected “b”. That would be incorrect, and here is why: While the relative frequency in this scenario is also 11 / 20 = 0.55, remember that the more repetitions that are performed, the closer the relative frequency gets to the probability it estimates. Here we perform only 20 repetitions, compared to 460 in the original survey.
Can you justify your answer and explain why other answers are incorrect?
A flight has been overbooked; however, there are 2 seats available—one in business class and one in first class. The ground crew decides to upgrade 2 of the coach (regular class) passengers so that 2 more passengers will be able to get on the flight. The crew has identified 4 passengers, 2 males and 2 females, who are traveling by themselves and who have been loyal frequent fliers on the airline. They decide to choose 2 of those passengers at random for the upgrade. The first chosen will be upgraded to first class, and the second chosen will be upgraded to business class. We’ll denote the 2 males and 2 females (as before) with M1, M2, F1 and F2.
What is the sample space in this case?
Which of the following is true?
It is important to note that it is not always the case the all the outcomes of a random experiment are equally likely!
A common mistake among students who are exposed to probability for the first time is to assume that all the outcomes of a random experiment are equally likely when in fact they are not.
Here is an example.
Example A fair coin is tossed repeatedly until the first ‘H’ is obtained but no more than three times. In this experiment there are four possible outcomes: Getting ‘H’ in the first toss, getting the first ‘H’ in the second toss, getting the first ‘H’ in the third toss, or tossing the coin three times without getting a ‘H’. The sample space in this case is therefore: {H, TH, TTH, TTT}.
As mentioned above, a common mistake is to wrongly assume that the four outcomes are equally likely, each with probability ¼.
Note that the first outcomes ‘H’ has probability ½ (since it represents the outcome of tossing the fair coin once and getting ‘H’). If the first outcome has probability ½, it is clear that the outcomes cannot be equally likely since the sum of the probabilities of all outcomes must be 1.