Carl is a big brother to newborn Lisa. Independently on any given day, there is
ID: 3307190 • Letter: C
Question
Carl is a big brother to newborn Lisa. Independently on any given day, there is a 5% chance that Lisa smiles at him. (Assume a month has 30 days for this problem and round all answers to 4 decimal places.)
Carl is a big brother to newborn Lusa. Independently on any given day, there is a 5% chance that Lisa smiles at hin. Assume a month has 30 days this problem and round all answers to 4 derna place a. What is the probability that Carl goes longer than a month without a smile from Lisa? Submit Answer Tncorrect. Tries 15 Previous Tries b. What Is the probability that Carl walts no more than two months to see a smile from LIsa? Submit Answer Tries o/S c. What is the prohability that Lisa smiles at Carl on exactly three days in a monthExplanation / Answer
a. Probability that Lisa smiles at Carl = 0.05
=> Probability that Lisa does not smile at Carl = 1 - 0.05 = 0.95
For Carl to go longer than a month, Lisa must not smile at him for atleast 31 days.
Probability that Lisa does not smile at Carl for 31 days = 0.9531 = 0.2039.
b. Let us first calculate the probability that Carl does not get a smile from Lisa in 60 days
= 0.9560 = 0.0461.
Therefore, the probability that Carl does not need to wait more than two months = 1 - 0.0461 = 0.9539.
c. The three days can come in 30C3 = 4060 ways.
Probability that Lisa smiles in those 3 days = 0.053 = 0.000125.
Probability that Lisa does not smile in the other days = 0.9527 = 0.2503.
=> Probability that Lisa smiles exactly 3 days = 4060 * 0.000125 * 0.2503 = 0.1270.