Title: CAT 2024 Slot 3 Quant Questions with Indian Game Solutions
Question: A game consists of 5 rounds. In each round, a player can either win or lose. The probability of winning a round is 0.4. What is the probability that a player wins at least 3 rounds?
Solution:
The probability of winning at least 3 rounds can be calculated by adding the probabilities of winning exactly 3, 4, and 5 rounds.
Probability of winning exactly 3 rounds = (Number of ways to choose 3 rounds out of 5) * (Probability of winning 3 rounds) * (Probability of losing 2 rounds)
= (5C3) * (0.4^3) * (0.6^2)
= 10 * 0.064 * 0.36
= 0.2304
Probability of winning exactly 4 rounds = (Number of ways to choose 4 rounds out of 5) * (Probability of winning 4 rounds) * (Probability of losing 1 round)
= (5C4) * (0.4^4) * (0.6^1)
= 5 * 0.0256 * 0.6
= 0.0768
Probability of winning exactly 5 rounds = (Number of ways to choose 5 rounds out of 5) * (Probability of winning 5 rounds) * (Probability of losing 0 rounds)
= (5C5) * (0.4^5) * (0.6^0)
= 1 * 0.01024 * 1
= 0.01024
Probability of winning at least 3 rounds = Probability of winning exactly 3 rounds + Probability of winning exactly 4 rounds + Probability of winning exactly 5 rounds
= 0.2304 + 0.0768 + 0.01024
= 0.31744
Question: A game has 10 players. The players are seated in a circle. In each round, a player is chosen randomly and asked to leave the game. The game continues until only 2 players remain. What is the probability that the first player to leave the game is the player sitting next to the host?
Solution:
The probability that the first player to leave the game is the player sitting next to the host can be calculated by considering the number of ways the host's neighbor can be chosen as the first player and dividing it by the total number of ways any player can be chosen as the first player.
Number of ways the host's neighbor can be chosen as the first player = 2 (since there are 2 players sitting next to the host)
Total number of ways any player can be chosen as the first player = 10 (since there are 10 players in total)
Probability = Number of ways the host's neighbor can be chosen as the first player / Total number of ways any player can be chosen as the first player
= 2 / 10
= 0.2
Question: A game consists of 4 players. Each player is dealt a card from a deck of 52 cards. What is the probability that all 4 players get a face card (King, Queen, or Jack)?
Solution:
The probability that all 4 players get a face card can be calculated by multiplying the probabilities of each player getting a face card.
Number of face cards in a deck = 12 (3 face cards for each of the 4 suits)
Total number of cards in a deck = 52
Probability of the first player getting a face card = 12/52
Probability of the second player getting a face card = 11/51 (since one face card has already been dealt)
Probability of the third player getting a face card = 10/50 (since two face cards have already been dealt)
Probability of the fourth player getting a face card = 9/49 (since three face cards have already been dealt)
Probability that all 4 players get a face card = (12/52) * (11/51) * (10/50) * (9/49)
= 0.004524
Question: A game has 3 players. Each player is dealt a card from a deck of 52 cards. What is the probability that the first player gets a heart, the second player gets a club, and the third player gets a diamond?
Solution:
The probability that the first player gets a heart, the second player gets a club, and the third player gets a diamond can be calculated by multiplying the probabilities of each player getting the desired suit.
Number of hearts in a deck = 13
Number of clubs in a deck = 13
Number of diamonds in a deck = 13
Total number of cards in a deck = 52
Probability of the first player getting a heart = 13/52
Probability of the second player getting a club = 13/51 (since one card has already been dealt)
Probability of the third player getting a diamond = 13/50 (since two cards have already been dealt)
Probability that the first player gets a heart, the second player gets a club, and the third player gets a diamond = (13/52) * (13/51) * (13/50)
= 0.012347
These are a few examples of CAT 2024 Slot 3 Quant questions with Indian game solutions. Good luck with your preparation!
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