Two Probability Question 1 . At a party, 100 guests check their hats at the entr

Question

Two Probability Question

1. At a party, 100 guests check their hats at the entrance. Mark is the first person to leave. He is drunk and takes away a hat at random. Each succeeding person takes his own hat if it is not taken. If it is taken, he picks a hat at random from the remaining hats. What is the probability that the last person gets his own hat?

2. There is a deck of 52 cards, and you pick one by one without replacement. You observe the past sequence and have one chance to stop and bet that the next card is red. Can you find a strategy that guarantees a probability of winning greater than 50%?

Explanation / Answer

1)

Last person will get his own hat only if the first person picks his own hat correctly. As there are 100 hats to choose from and only 1 hat is the correct hat, probability that Mark chooses his own hat is 1/100

Hence probability that last person gets his own is 1/100 i.e. 0.01

2)

Count the number of cards in past sequence, if the number of black cards are more than number of red cards in the past sequence, this means the remaining cards have more number of red cards than black cards. This will increase the probability of winning more than 50% on betting.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.