Probability Final Review

1.One marble is drawn at random from a bag containing 2 white, 4 red, and 6 blue marbles Find the probability: One – Basic sixth grade probability…… a. It is not white b. It is either red or white

1. A fair coin is tossed five times. Not one…Not basic First toss…..two possibilities Second toss…..two possibilities Therefore…..BINOMIAL a. Find the probability that exactly three heads appear b. Find the probability that at least one heads appears P(at least one heads) = 1 – P(no heads)

2.A bag contains two red, four yellow, and six blue marbles. Two marbles are drawn at random. Find the probability that Both are blue. Not one…not basic First Draw…12 possibilities Second Draw…11 possibilities Therefore…..COMBINATIONS

2.A committee of five men and four women are on the…. If four of them are selected at random…find the probability… Committee…Combinations a. b. At least three of them are menTHREE MEN or FOUR MEN There are no men on the committee

3.Three cards are drawn at random from a 52 card deck. Find The probability Not one…not basic First draw…52 possibilities Second draw…51 possibilities Therefore COMBINATIONS a. b. All three are red All three are of the same suit

3. A pair of fair dice is tossed three times Not one…Not basic First toss…36 possibilities Second toss…36 possibilities Therefore…BINOMIAL a. Find the probability that the sum of 7 appears three times. 16, 25, 34, 43, 52, 61 – six winners b. Find the probability that the sum of 11 never appears 65, 56 – two winners

4. Two die are rolled. Find the probability What are we looking at? a. The sum of the numbers is 9 36, 45, 54, 63 – four winners Basic b. Either the sum of the numbers is 6 or both numbers up are 4. 15, 24, 33, 42, 51 OR 44 – six winners

4. Two cards are drawn…Find the probability…. Not one…not basic First draw…52 possibilities Second draw…51 possibilities Therefore COMBINATIONS a. Both black or both jacksb. Both either black or a jack c. Both are black or both are face cards

5.If a set of six books is placed randomly on a shelf, what is The probability that they will be arranged in either correct order Or reverse order? 1 + 1

5. An unfair coin…P(heads) = 4/5, P(tails) = 1/5 a. If..tossed four times, find the probability of at least three tails First toss…2 possibilities Second toss…2 possibilities Therefore…BINOMIAL three tails OR four tails + b. If…tossed six times, find the probability of at least one heads P(at least one heads) = 1 – P(no heads)

7.A box contains (1-20). A slip of paper is drawn. Find the Probability: One….basic a. It is less than zero b. It is a positive integer less than 21.

8.A bag contains 6 blue, 4 red and 2 white. Yugo pulls out one Disc, replaces it, and pulls out a second disc. Find the probability Not one….not basic First draw…12 possibilities Second draw…12 possibilities Therefore…BINOMIAL a. One disc is blue and one is white b. Each disc is red