Objectives Find entries in Pascal’s triangle. Use Pascal’s triangle to find combinations and probabilities.

11.7 Pascal’s Triangle Glossary Term Pascal’s triangle

Rules and Properties Patterns in Pascal’s Triangle Row n contains n + 1 entries. The kth entry in row n is nCk – 1. The sum of entries in row n is 2n. nCk – 1 + nCk = n + 1Ck , where 0 < k  n

Rules and Properties Pascal’s Triangle and Two-Outcome Experiments Perform n independent trials. There are 2 equally likely outcomes. Probability of event A occurring exactly k times: P(A) = nCk 2n

Key Skills Find entries in Pascal’s triangle. Find the fourth entry in row 9. n = 9; k = 4; k – 1 = 3 9! 6!3! nCk – 1 = 9C3 = = 84

Key Skills Use Pascal’s triangle to find probabilities. You guess all the answers to 10 questions on a true-false test. Find the probability of getting exactly 6 or exactly 7 correct answers. number of possible outcomes: 210

Key Skills Use Pascal’s triangle to find probabilities. 10 questions probability of exactly 6 or exactly 7 correct? number of possible outcomes: 210 10C6 210 210 1024 = P(exactly 6 correct) =  0.21 10C7 210 120 1024 = P(exactly 7 correct) =  0.12

Key Skills Use Pascal’s triangle to find probabilities. 10 questions probability of exactly 6 or exactly 7 correct? number of possible outcomes: 210 P(exactly 6 correct)  0.21 P(exactly 7 correct)  0.12 P(exactly 6 or 7 correct)  0.21 + 0.12 = 0.33 TOC