You’re in NY and are trying to flag down a cab. The chance of catching a cab on your street is 25% per minute of standing there. What is the probability that you will still be there after: i. 1 minute? ii. 2 minutes? b) What is the probability that you caught a cab in the 2nd minute? c) What is the probability that you didn’t catch a cab in the 2nd minute?

What is the probability that you will still be there after: P(C1) = 4/16 P(C1) = 1/4 P(S1 C2) = 3/16 C1 C2 P(C1) = 0.25 P(C2|S1) = 0.25 P(S1 S2) = 9/16 S1 S2 P(S1) = 0.75 P(S2 | S1) = 0.75 P(S1) = 3/4 What is the probability that you will still be there after: i. 1 minute? 3/4 ii. 2 minutes? 9/16 b) What is the probability that you caught a cab in the 2nd minute? 3/16 c) What is the probability that you didn’t catch a cab in the 2nd minute? 13/16

The Jones family has 2 parents, 4 kids, 2 cats, 3 dogs The Jones family has 2 parents, 4 kids, 2 cats, 3 dogs. 5 people/animals go on a walk. It is known that at least 1 parent went and at least 1 pet went. How many different scenarios are there for who went?

P1,P2 K1,K2,K3,K4 C1,C2,D1,D2,D3 (11 total) 0 animals >0 animals 0 parents >0 parents 1 parent 2 parents Method 1: total – [(0P,0A) + (>0P,0A) + (0P,>0A)] 11c5 – [0 + 6c5 + 9c5] = 462 – [0 + 6 + 126] = 330 Method 2: (>0P, >0A) = (1P,4A,0K) + (1P,3A,1K) + (1P,2A,2K) + (1P,1A,3K) + (2P,3A,0K) + (2P,2A,1K) + (2P,1A,2K) (2c1)*(5c4)*(4c0) + (2c1)*(5c3)*(4c1) + (2c1)*(5c2)*(4c2) + (2c1)*(5c1)*(4c3) + (2c2)*(5c3)*(4c0) + (2c2)*(5c2)*(4c1) + (2c2)*(5c1)*(4c2) = 330