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19 Jul 2022, 08:00
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Difficulty:
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23% (02:04) correct
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wrong
based on 88
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Ronaldo puts an orange, an apple and a banana in each of his 4 children's lunch boxes. The 5th child runs into the kitchen and randomly grabs one fruit from each of the 4 bags. What is the probability that she got exactly 2 different types of fruit ?
(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27
(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27
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19 Jul 2022, 08:13
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Bunuel
Ronaldo puts an orange, an apple and a banana in each of his 4 children's lunch boxes. The 5th child runs into the kitchen and randomly grabs one fruit from each of the 4 bags. What is the probability that she got exactly 2 different types of fruit ?
(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27
(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27
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There are 3 choices for the first fruit, 3 for the second, 3 for the third, and 3 for the fourth, so 3*3*3*3 = 81 total possibilities.
We can find the number of ways of getting exactly two fruits:
1 of one fruit and 3 of another:
1 apple + 3 bananas = 4 ways
1 apple + 3 oranges = 4
1 b + 3 a = 4
1 b + 3 o = 4
1 o + 3 a = 4
1 o + 3 b = 4
That's 24 ways.
2 of one fruit and 2 of another:
2 apples + 2 bananas = AABB, ABAB, ABBA, BAAB, BABA, BBAA = 6
2 a + 2 o = 6
2 b + 2 o = 6
That's 18 ways.
24+18 = 42
42/81 = 14/27
Answer choice D.
Updated on: 20 Jul 2022, 08:08
Originally posted by Archit3110 on 19 Jul 2022, 09:10.
Last edited by Archit3110 on 20 Jul 2022, 08:08, edited 1 time in total.
Last edited by Archit3110 on 20 Jul 2022, 08:08, edited 1 time in total.
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fruits are O,A,B and 4 bags so total fruits are 12
and P of drawing a fruit from 4 bags is 3^4 ; 81 and ways how these fruits can be drawn is 4c1
exactly 2 different types of fruit possibility
(o,o,o,a) ( o,o,o,b) ;(a,a,a,o) ( a,a,a,b) ; (b,b,b,o) ( b,b,b,a)
this can be arranged in4ways and total possibilities 24 as we have 6 such cases
(o,o,a,a) ( o,o,b,b)
(a,a,o,o) ( a,a,b,b)
(b,b,o,o) ( b,b,a,a)
4!/2!*2! ; 6 *3 ; 18
total 18+24 ; 42
42/81 ; 14/ 27
option D
and P of drawing a fruit from 4 bags is 3^4 ; 81 and ways how these fruits can be drawn is 4c1
exactly 2 different types of fruit possibility
(o,o,o,a) ( o,o,o,b) ;(a,a,a,o) ( a,a,a,b) ; (b,b,b,o) ( b,b,b,a)
this can be arranged in4ways and total possibilities 24 as we have 6 such cases
(o,o,a,a) ( o,o,b,b)
(a,a,o,o) ( a,a,b,b)
(b,b,o,o) ( b,b,a,a)
4!/2!*2! ; 6 *3 ; 18
total 18+24 ; 42
42/81 ; 14/ 27
option D
Bunuel
Ronaldo puts an orange, an apple and a banana in each of his 4 children's lunch boxes. The 5th child runs into the kitchen and randomly grabs one fruit from each of the 4 bags. What is the probability that she got exactly 2 different types of fruit ?
(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27
(A) 1/3
(B) 4/9
(C) 13/27
(D) 14/27
(E) 16/27
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