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27 May 2025, 00:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
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Question Stats:
64% (02:51) correct
36%
(03:06)
wrong
based on 99
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Two identical urns—black and white—each contain 5 blue, 5 red and 10 green balls. Every ball selected from the black urn is immediately returned to the urn, while each ball selected from the white urn is removed and placed on a table. If Jenny receives a quarter for every blue ball, a dime for every red ball and a nickel for every green ball she selects, what is the probability that she will be able to buy a 25-cent candy bar with the proceeds from drawing four balls—two from each urn?
A) 143/152
B) 143/154
C) 121/180
D) 271/965
E) 152/1000
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
A) 143/152
B) 143/154
C) 121/180
D) 271/965
E) 152/1000
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
27 May 2025, 03:44
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Given the info, the only case where Jenny won't be able to secure 25 cent is when she gets all greens in 4 draws, as they will amount to only 20 cents
P(all green) = 10/20 *10/20 *10/20 *9/19 = 9/152
P(not all green) = 1 - 9/152 = 143/152
P(all green) = 10/20 *10/20 *10/20 *9/19 = 9/152
P(not all green) = 1 - 9/152 = 143/152
Bunuel
General Discussion
27 May 2025, 01:11
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Two identical urns—black and white—each contain 5 blue, 5 red and 10 green balls. Every ball selected from the black urn is immediately returned to the urn, while each ball selected from the white urn is removed and placed on a table.
If Jenny receives a quarter for every blue ball, a dime for every red ball and a nickel for every green ball she selects, what is the probability that she will be able to buy a 25-cent candy bar with the proceeds from drawing four balls—two from each urn?
Let number of blue, red and green balls selected be b, r & g respectively
Conditions not to achieve the goal: -
25b + 10r + 5g < 25
b + r + g = 4
b=0; 10r+5g < 25 ; 2r + g < 5;
r + g = 4; g = 4 - r; 2r + 4 - r < 5; r<1; r = 0
Both blue balls and red balls should not be selected to not achieve the goal
Probability of not achieving the goal = (10/20)(10/20)(10/20)(9/19) = 9/152
Probability of achieving the goal = 1 - 9/152 = 143/152
IMO A
If Jenny receives a quarter for every blue ball, a dime for every red ball and a nickel for every green ball she selects, what is the probability that she will be able to buy a 25-cent candy bar with the proceeds from drawing four balls—two from each urn?
Let number of blue, red and green balls selected be b, r & g respectively
Conditions not to achieve the goal: -
25b + 10r + 5g < 25
b + r + g = 4
b=0; 10r+5g < 25 ; 2r + g < 5;
r + g = 4; g = 4 - r; 2r + 4 - r < 5; r<1; r = 0
Both blue balls and red balls should not be selected to not achieve the goal
Probability of not achieving the goal = (10/20)(10/20)(10/20)(9/19) = 9/152
Probability of achieving the goal = 1 - 9/152 = 143/152
IMO A
