We are expected to know the Binomial Theorem.For , determine
(a) the middle term
(b) the term containing
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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.
The opposite of "at least one Black" is "no Blacks".(b) What is the probability that you draw at least 1 black ball?
To get no Blacks, we want 6 of the 13 Others: . ways.
. . Hence: .