A student guesses at all 5 questions on a true-false quiz. Find each probability. P( all 5 cor

A student guesses at all 5 questions on a true-false quiz....

Key Concepts

Uniform Probability Distribution

This idea applies when every outcome in a set has an equal chance of occurring, such as the two possibilities in a true-false question. It ensures that the probability for each answer is the same, allowing for straightforward computation of probabilities through multiplication.

Independent Events

This concept means that the outcome of one event does not affect the outcome of another. In the context of guessing quiz answers, each question is considered an independent event because the chance of answering any single question correctly does not depend on the answers to previous questions.

Multiplication Principle of Probability

This principle is used when calculating the probability of a series of independent events all occurring. It states that the probability of several independent events happening together is the product of their individual probabilities, which is essential when determining the likelihood of getting all answers correct.

Transcript

00:01 So, we are being asked a probability question here, but specifically we're being asked about five questions on a true or false quiz.

00:09 Now, it's extremely important here that we understand this is a true or false quiz.

00:15 That's why they gave us that information as opposed to a multiple choice quiz or something like that.

00:19 The point of them saying it's a true or false quiz is that it means there are only two options.

00:26 It's a binary decision.

00:28 You're either going to get it right or you're going to get it right.

00:31 It wrong because it does say the student is guessing so it's not like you're leaving any these blank right it does clearly say the student guesses so you're assuming that there is an answer put by he or she in that case it's a 50 -50 shot every single time right because you're either going to get it right or get it wrong so because of that that makes this a binomial distribution problem or a problem that we can solve using the binomial distribution because we can use this for any time you have a binary situation a situation where there are only two outcomes, okay, hence the by and binomial right, that's a prefix for two.

01:06 So we have our formula here, the binomial distribution which you guys should have seen already because this is the review part where it's going back to 12 -8 so it is assuming that you've already done that before.

01:18 It's not what this section was about, it's what an earlier section was about.

01:21 So what we've got here is that your probability for your scenario is going to be equal to the combination of n being the number of trials and x being the number of successes.

01:33 So n is like the total amount of the trials that you're doing and x is whatever you're wanting to get, whatever the question is asking you about.

01:42 Then you've got p to the x.

01:44 So p is the probability of you having success to the power of x which we already said was the number of successes.

01:52 Then that's times q which is the probability of failure and that's being taken to the power of n minus x so the number of trials minus the number of successes.

02:02 Meaning basically how many times do you not need to succeed? so if we look at this specific problem, so we've got five questions.

02:10 Okay, so right off the bat there, that's how many questions we have.

02:14 That means that's our total, that's end.

02:17 That's the number of trials, quote unquote, that we're running, because you've got five chances to get a right answer, right? for this specific problem, it wants us to find the probability that you get all five correct, meaning we have five trials that's n that would have been the same no matter what question we were doing as long as this scenario is five questions on the quiz that also is giving us x though because it's saying it wants us to get all five correct meaning it wants us to have five successes okay so then the other two variables that we need are p and q well p represents the probability of success...

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