[lego2401]

Point for discussion:

From what I've seen on the forum in the last while, the sticky parts in probability are,

1-when to use combinations vs not to, or when they can be used interchangebly, and

2- When asked to find the probability of "atleast" a certain event, when to double count and when not to:

Here are examples of the second point:

A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

In this instance, we take 3 situations, namely where the first is blue, second not blue,
or first is not blue, second is not blue,
or both are blue.

Now in the second example,

A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is the probability that at least one marble is blue?

In this instance, we approach the problem by counting the sitation where none are blue, that is, both red.

The point I see mistakes in is, when the two are of different colors, we count twice, ie, we consider RB then BR, whereas when the two are of the same color, we count only once.

Let's discuss these points and see if anyone has some kind of fixed rather than adhoc approach.

Finally, problem to work with (this is a variation of one of the problems in Grey's document):

Seven beads are in a bag: three blue, two red, and two green. If three beads are randomly drawn from the bag, what is the probability that NONE of them are blue?