1. In a deck of cards, Kings, Queens and Jacks are called the face cards. If 4 cards are randomly chosen together, what is the probability that at least one of the cards is a face
card? [Composition of a standard 52-card deck]
2. Suppose, 10 students have been selected for the prestigious Sir Abed Scholarship for
their excellent performances in extracurricular activities and academic results. Let’s say,
there are 4 types of award: A (100% +), B (100%), C (97%) and D (95%) . Also, a
student has an equal chance of getting any of these 4 scholarships. What is the
probability that exactly 4 of the 10 students get A and 3 students get C?
3. Suppose, you are attending an exam where there are 9 multiple choice questions with 3
options in each. A question can have multiple correct answers, and in that case, you
have to check all of the correct answers to get the question right.
a. What is the probability that you’ll get exactly 6 of the questions right?
b. What is the probability that you’ll get at most 6 of the questions right?
4. What is the maximum number of people in a gathering such that the probability of two
people having the same birthday doesn’t exceed 60%?
5. Suppose twin brothers, Lim and Jim are taking part in an experiment called ‘Twin’s
Telepathy Test’. In this test, 5 candles of different colors are shown to both the brothers
in the beginning. Then, the twins are put into two different rooms and the candles are
given to Jim. He picks a candle himself, presses a buzzer to let Lim know that one
candle’s been picked without telling him the color of the candle. Then Jim tries to
connect to Lim through his mind and transmit the name of the color to Lim telepathically.
Now, Lim has to guess the color of the candle. This goes on for 5 times for all five
candles.
a. What is the probability that Lim makes exactly 4 right guesses?
b. The same experiment is repeated, but this time after each wrong guess Lim makes,
the correct answer is shown to him. Now what is the probability that Lim makes
exactly 4 right guesses?
6. Suppose there are 8 fair coins and 12 unfair coins in a bag such that the unfair coins
have a 75% probability of landing heads. A coin is randomly picked from the bag and
flipped 9 times. If the coin landed heads 7 times out of 9, what is the probability that the
coin is unfair?