60% students in a school take neither calculus nor...

60% students in a school take neither calculus nor probability course. 20% of students take calculus. 30% take probability. If one of the students is chosen randomly from this school, what is the probability that this student takes (a) calculus and probability? [6 points] (b) either calculus or statistics (but not both)? [6 points] (c) Are the events {a randomly picked student takes calculus} and {a randomly picked student takes probability} independent? Why? [6 points] [Hint: Draw a Venn diagram to visualize set calculations.]

Transcript

00:01 Hi, i'm david and i'm here to have you answer your question.

00:03 Let me bring up your question here.

00:07 In this question we will recall about the concept of the independent.

00:12 Let me remind you that the a and b are independent.

00:22 If the probability to the a intersection b, it must equal to the probability to the a times the probability of the b.

00:31 And in this question let me try to summarize the question by the venn diagram.

00:39 So here 60 % of the students in school take neither calculus no probability causes.

00:47 So means that we will have the first circle which stands from the calculus.

00:54 The second circle stands for the probability.

00:57 60 % students in school take neither of them.

01:02 So no c nor b so the outside probability equal to the 0 .6 that will be something we need to be careful outside here means that i will make it clear here outside will be this one we don't include the inside between of them that will be outside and the outside it will equal to the 0 .6 so this one equal to the 0 .6 and now we will have 20 % of students take calculus so we know that calculus the whole thing in the in the blue here sorry i will draw in blue again in blue it will equal to the c equal to 0 0 .2 and then 30 % taking the probability so b here equal to 0 .3 and now if one understand the students what is a probability that this student text so in the a probability of the calculus and probability so it means that and there so let me remind you another formula here probability of the a union b it will equal to the probability of the a plus the probability of the b minus probability of the a in the section b so from here it will apply the formula should get this one equal to the probability a this one will be the c union b and then i bring this one to the other side and then we should get it will be sorry there will be the probability of the b plus probability of the b i technically i will be b here then minus the union between them so it will be c and then union the b now we know the probability of the c equals to the 0 .2.

03:18 We know the probability of the b equals 0 .3.

03:22 Now the union between them is not to do it...

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