Hello, john002!

We are expected to know the Binomial Theorem.For , determine

(a) the middle term

(b) the term containing

. . . . . . . .

. . . . . . .

There are 52 cards in a standard deck of cards.You are dealt one card from a standard deck of playing cards.

a) What is the probability that the card is 5?

b) What is the probability that the card is a 8 or a club?

(a) Four of them are 5's.

. .

(b) There are four 8's: .

. . .There are 13 Clubs: .

. . .But don't count the twice!

Hence, there are 16 cards that are an 8 or a Club.

. .

There are: . possible outcomes.A box contains 5 black balls, 4 red balls, 4 green balls, and 5 blue balls.

You select 6 balls from the box without replacing them.

(a) What is the probabilty that you select excatly 3 black balls?

We have: .5 Black balls and 13 Others

We want: 3 Black balls and 3 Others.

There are: . ways to pick 3 Black.

There are: . ways to pick 3 Others.

Hence, there are: . ways to pick 3 Blacks and 3 Others.

Therefore: .

The opposite of "at least one Black" is "(b) What is the probability that you draw at least 1 black ball?Blacks".no

To get no Blacks, we want 6 of the 13 Others: . ways.

. . Hence: .

Therefore: .