A survey was conducted from a large group of high school...

A survey was conducted from a large group of high school students in an effort to determine what science courses they were currently enrolled in. It was found that 60% of the students were enrolled in Chemistry, 66% of students were enrolled in Physics, and 46% of students were enrolled in Biology. Assume independence between the science classes that each student is enrolled in. (a) What is the probability that a randomly selected student is enrolled in Chemistry and Physics, but not Biology? (b) What is the probability that a randomly selected student is enrolled in Physics but not Chemistry? (c) What is the probability that a randomly selected student is enrolled in Chemistry or Biology?

Transcript

00:01 Hello, so i'm going to answer your question about probabilities and the specific probabilities for students enrolling science classes.

00:09 For doing so, i divide the questions in the different sub -questions and then i'm going to explain you the logic behind it.

00:15 So the first question is, what is the probability that randomly selected students enrolled in chemistry and physics but not biology? for doing so, i first found the probabilities that i need to calculate.

00:28 So the first is the probability in rolling chemistry.

00:32 This is given here and this is here.

00:35 I just pass it to from percent of terms to terms of probability, dividing it by a hundred, then the probability of being in physics that is here.

00:46 And then the probability of being not in biology.

00:49 So as you may recall from statistics, the probability of one event is also the probability of one minus the probability of the other possibilities in this case you have the probability of being in biology so you just have to take the complement and this will give you a probability of not being in biology so i make this is 1 minus the probability of being in biology that is 46 % this will be results 0 .54 and now i have to multiply each situation because you want to understand what are the probability that these three events should happen so it will be 0 .6 times 0 .66 times 0 .54 this will be resolved 0 .2184.

01:35 The second question is what is a probability that random selected the student isn't running physics but not in chemistry so i apply the same logic so for physics do i just take the probability that is given in the problem and for not chemistry i just take one minus the in your case chemistry of 0 .6 so using this same logic i get the complement 0 .4 and then i multiply it so this would be the probability 0 .66 times 0 .4.

02:04 Now for the final question i need to make an additional assumption that is that what is a probability that a random selected student is enrolled in chemistry or biology as you may understand a student can be enrolled in both situations in both occasions in chemistry and biology or even enrolling both classes...

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