The article "Scrambled Statistics: What Are the Chances of...

Name: Problem 1, Chapter 5: Statistics Learning From Data
Uploaded: 2021-04-19T15:48:35-08:00
Duration: 4 min 36 s
Channel: Matthias Wuest
Description: The article "Scrambled Statistics: What Are the Chances of Finding Multi-Yolk Eggs?" (Significance [August 2016]: 11) gives the probability of a double-yolk egg as 0.001 . a. Give a relative frequency interpretation of this probability. b. If 5000 eggs were randomly selected, about how many double-yolk eggs would you expect to find?

The article "Scrambled Statistics: What Are the Chances of Finding Multi-Yolk Eggs?" (Significance [August 2016]: 11) gives the probability of a double-yolk egg as 0.001 . a. Give a relative frequency interpretation of this probability. b. If 5000 eggs were randomly selected, about how many double-yolk eggs would you expect to find?

The article "Scrambled Statistics: What Are the Chances of Finding Multi-Yolk Eggs?" (Significance [August 2016]: 11) gives the probability of a double-yolk egg as 0.001 .
a. Give a relative frequency interpretation of this probability.
b. If 5000 eggs were randomly selected, about how many double-yolk eggs would you expect to find?

Key Concepts

Probability

Probability is a measure used to quantify the chance that a given event will occur, ranging between 0 and 1. It provides a numerical representation of the likelihood of events, where a value like 0.001 indicates a 0.1% chance of the event happening.

Relative Frequency Interpretation

The relative frequency interpretation of probability suggests that if an experiment or trial is repeated many times, the proportion of times the event occurs will approximate the probability of the event. In this context, it means that if you observe a large number of eggs, about 0.1% of them are expected to be double-yolk eggs.

Expected Value

Expected value is a concept in probability that determines the average outcome if an event or process is repeated a large number of times. For a given probability, multiplying it by the number of trials (or eggs, in this case) yields the expected number of occurrences of the event. For instance, for 5000 eggs with a probability of 0.001, the expected number of double-yolk eggs would be 5.

Transcript

00:01 All right, so this problem is a really interesting application of bay theorem because it deals with overlapping events in a way.

00:06 So firstly, let's define a couple of events.

00:09 We're talking about whether eggs are broken or not in a carton.

00:13 So let's define event a as non -broken.

00:16 All right, let's define event b as one, say exactly one broken.

00:25 And then c and d will be two and three broken respectively.

00:28 So c will be exactly two broken.

00:30 And you'll see why the exactly is important in just a sec.

00:36 And we're told that the probability that exactly four are broken or more is negligible.

00:43 All right.

00:44 So we're also given associated probabilities for these, right? we're given that the probability of a, we're given that the probability of a is 0 .75, given that the probability of b is 0 .192.

01:01 Let me put an equal sign there.

01:03 Probability of c is equal to 0 .022, that's 2 .2%.

01:08 And the probability of d is equal to 0 .001, or rather 0 .1%.

01:16 Now we are asked, and this is often the tricky part of the question.

01:22 We are told that an egg is selected at random from a carton, and it is found to be broken.

01:27 So there is a broken egg.

01:28 I'm literally going to type that.

01:30 There is a broken egg.

01:33 And we are asked, what is the probability that this egg is the only one broken? so firstly, we want, what is the probability that there is exactly one broken egg given that you are holding in your hand a broken egg? okay, so given that there is at least one broken.

01:56 We know that.

01:57 We're holding it...

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