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Red pen, highlighter, GP notebook, calculator U11D14 Have out: Bellwork: Solve the following: 1) A coin is tossed 10 times. what is the probability of getting at most 2 H? 2) Using a standard deck of cards, what is the probability of getting 2 jacks in a 5–card hand? Expand the following: 3) (x – 2y)5 total:

Solve the following: 1) A coin is tossed 10 times. what is the probability of getting at most 2 H? P (at most 2 H in 10 tosses) +3 +1 +2 0H 1H 2H 3H 4H 5H 6H 7H 8H 9H 10H row 10 

# of ways to get 2 cards from all jacks Solve the following: 2) Using a standard deck of cards, what is the probability of getting 2 jacks in a 5–card hand? # of ways to get 2 cards from all jacks # of ways to get 3 other card (non–jacks) +2 P (2 jacks) = +1 Total # of possible 5–card hands +2

Use Pascal’s Triangle… or combinations. = (x + (–2y))5 Expand the following: 3) (x – 2y)5 Use Pascal’s Triangle… or combinations. = (x + (–2y))5 x5 (–2y)0 x4 (–2y)1 x3 (–2y)2 x2 (–2y)3 x1 (–2y)4 x0 (–2y)5 1______ + 5______ + 10______ + 10______ + 5______ + 1______ x5 x4 (–2y) x3 (4y2) x2 (–8y3) x1 (16y4) (–32y5) 1___ + 5_______ + 10_______ + 10_______ + 5_______ + 1_____ = x5 – 10x4y + 40x3y2 – 80x2y3 + 80xy4 – 32y5 +6 +1 Start with row 5 of Pascal’s triangle. +1 Write powers of x in descending order. +1 Write powers of (–2y) in ascending order. total: row 5 

It’s time for the study team test! Move into your group and work on the test. Due tomorrow!

Expand the following: 3) (4x + 3y)3 Use Pascal’s Triangle… or combinations. (4x)3 (3y)0 (4x)2 (3y)1 (4x)1 (3y)2 (4x)0 (3y)3 = 1 _________ + 3 _________ + 3 _________ + 1 _________ (64x3) (16x2) (3y) (4x) (9y2) (27y3) = 1 _________ + 3 _________ + 3 _________ + 1 _________ = 64x3 + 144x2y + 108xy2 + 27y3 row 3 