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Wittaler [7]
3 years ago
12

A cooler has 12 apple juices and 15 grape juices. 9 of the apple juices are sugar free and 5 of the grape juices are sugar free.

A juice is chosen at random. Given that the juice is NOT sugar free, find the probability that it is grape juice. A) 10 13 B) 15 27 C) 2 3 D) 3 4
Mathematics
1 answer:
Fantom [35]3 years ago
7 0

altogether there are 27 juices

probability of apple juice = 12/27

probability of grape juice = 15/27

probability of sugar free = 14/27

probability of not sugar free = 13/27

They already said the juice that is chosen is definitely NOT sugar free, so we dont need to include the probability of that because we already know it.

apple juice = 12

sugar free = 9

12 - 9 = 3 not sugar free

grape juice = 15

sugar free = 5

15 - 5 = 10 not sugar free

we need the not sugar free ones, so 3 + 10 = 13

out of 13 not sugar free, 10 are grape juice, so the probability of not sugar free grape juice = 10/13, so the answer is A)

srry if this is too long, i take too long to explain things, but i hope this still helps

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Answer:

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Step-by-step explanation:

To show that the function f defined above is a bijective function, we need to prove that f is well defined, injective and surjective.

f   is well defined:

To see this, we need to show that f sends elements fromo b9 to elements of E10. first note that f(a) has 1 more binary integer than a, thus, it has 10. if a has an even number of 1's, then f(a) also has an even number because a 0 was added. On the other hand, if a has an odd number of 1's, then f(a) has one more 1, as a consecuence it will have an even number of 1's. This shows that, independently of the case, f(a) is an element of E10. Thus, f is well defined.

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If a and b are 2 different binary strings, then f(a) and f(b) will also be different because the first 9 elements of f(a) form a and the first elements of f(b) form b, thus f(a) is different from f(b). This proves that f in injective.

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This shows that f is well defined from B9 to E10, injective, and surjective, thus it is a bijection.

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