Asked by Tyler Schatz on Jun 02, 2024
Verified
A chess set has 16 white pieces and 16 black pieces.Half of the pieces of each color are pawns.Suppose that you are blindly removing chess pieces from a bag.What is the probability that the first three pieces you draw will not be 3 black pawns?
A) 29/32
B) 319/336
C) 613/620
D) 13/16
E) 37/64
Chess Set
A collection of game pieces and board used to play chess, consisting of 32 pieces: 16 each for two players, including kings, queens, rooks, bishops, knights, and pawns.
Probability
The measure or assessment of the likelihood of a particular event or outcome happening based on available evidence or statistical analysis.
- Acquire the ability to compute probabilities related to combinations and permutations within given contexts.
Verified Answer
MT
Marwa TaqatqaJun 08, 2024
Final Answer :
C
Explanation :
There are a total of 32 pieces in the bag, and half of each color (16/2) are pawns, so there are 8 black pawns and 8 white pawns.
The probability that the first piece you draw is not a black pawn is 24/32 (there are 8 black pawns out of 32 total pieces).
After drawing a piece, there will be 31 pieces left in the bag, with 7 black pawns remaining. So the probability that the second piece you draw is not a black pawn is 23/31.
Similarly, the probability that the third piece you draw is not a black pawn, given that the first two were not black pawns, is 22/30.
Therefore, the probability that the first three pieces you draw will not be 3 black pawns is:
(24/32) x (23/31) x (22/30) = 613/620.
Thus, the answer is C.
The probability that the first piece you draw is not a black pawn is 24/32 (there are 8 black pawns out of 32 total pieces).
After drawing a piece, there will be 31 pieces left in the bag, with 7 black pawns remaining. So the probability that the second piece you draw is not a black pawn is 23/31.
Similarly, the probability that the third piece you draw is not a black pawn, given that the first two were not black pawns, is 22/30.
Therefore, the probability that the first three pieces you draw will not be 3 black pawns is:
(24/32) x (23/31) x (22/30) = 613/620.
Thus, the answer is C.
Learning Objectives
- Acquire the ability to compute probabilities related to combinations and permutations within given contexts.