Addition Rule and Venn Diagrams

Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. If five students are in both classes, how many students are in neither class?

Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. If five students are in both classes

How many are in either class?

Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. If five students are in both classes.

 What is the probability that a randomly-chosen student from this group is taking only the Chemistry class?

Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. If five students are in both classes.

What is the probability that you do not take English?

Suppose my friend discovered that her cat had a taste for the adorable little geckoes that live in the bushes and vines in her yard in Arizona. In one month, suppose he deposited the following on her carpet: six gray geckoes, twelve geckoes that had dropped their tails in an effort to escape capture, and fifteen geckoes that he'd chewed on a little. Only one of the geckoes was gray, chewed on, and tail-less; two were gray and tail-less but not chewed on; two were gray and chewed on but not tail-less. If there were a total of 24 geckoes left on her carpet that month, and all of the geckoes were at least one of "gray", "tail-less", and "chewed on", how many were tail-less and chewed on but not gray?

What does it mean for two events to be mutually exclusive? Give one example of two events that are mutually exclusive.

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If two events are mutually exclusive, then which of the following is true?

• $P\left(A\cup B\right)=0$

• $The\ venn\ diagram\ has\ only\ two\ none\ overlapping\ circles$

• $P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)=P\left(A\right)+P\left(B\right)$

• $P\left(A\cap B\right)=P\left(A\right)\cdot P\left(B\right)$

A single card is drawn from a deck. Find the probability that it is a king or a club.

In a hospital unit there are eight nurses and five physicians. Seven nurses and three

physicians are females. If a staff person is selected, find the probability that the subject

is a nurse or a male.