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One-third of 12 oranges got rotten. If 4 oranges are taken out randomly, what is the probability that all orange are rotten?
- a)14/995
- b)1/495
- c)16/495
- d)8/495
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
One-third of 12 oranges got rotten. If 4 oranges are taken out random...
To solve this problem, we need to first determine the total number of oranges that got rotten, and then calculate the probability of selecting all rotten oranges from the given selection.
Determining the total number of rotten oranges:
One-third of 12 oranges got rotten, which means (1/3) * 12 = 4 oranges got rotten.
Calculating the probability of selecting all rotten oranges:
Out of the 12 oranges, 4 have already been determined as rotten. So, we have a total of 12 - 4 = 8 oranges remaining from which we need to select 4.
Now, let's calculate the probability step by step:
Step 1: Determine the total number of ways to select 4 oranges from the remaining 8.
The total number of ways to select 4 oranges from 8 is given by the combination formula C(n, r) = n! / (r! * (n-r)!), where n is the total number of objects and r is the number of objects to be selected.
In this case, n = 8 and r = 4, so the total number of ways is C(8, 4) = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70.
Step 2: Determine the number of ways to select all 4 rotten oranges from the remaining 8.
Since all 4 oranges are rotten, we need to select all 4 from the remaining 8. So, the number of ways is C(8, 4) = 70.
Step 3: Calculate the probability by dividing the number of favorable outcomes (selecting all rotten oranges) by the total number of possible outcomes (selecting any 4 oranges from the remaining 8).
Probability = Number of favorable outcomes / Total number of possible outcomes = 70 / 70 = 1.
Therefore, the probability that all oranges selected are rotten is 1/495, which corresponds to option B.
Determining the total number of rotten oranges:
One-third of 12 oranges got rotten, which means (1/3) * 12 = 4 oranges got rotten.
Calculating the probability of selecting all rotten oranges:
Out of the 12 oranges, 4 have already been determined as rotten. So, we have a total of 12 - 4 = 8 oranges remaining from which we need to select 4.
Now, let's calculate the probability step by step:
Step 1: Determine the total number of ways to select 4 oranges from the remaining 8.
The total number of ways to select 4 oranges from 8 is given by the combination formula C(n, r) = n! / (r! * (n-r)!), where n is the total number of objects and r is the number of objects to be selected.
In this case, n = 8 and r = 4, so the total number of ways is C(8, 4) = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70.
Step 2: Determine the number of ways to select all 4 rotten oranges from the remaining 8.
Since all 4 oranges are rotten, we need to select all 4 from the remaining 8. So, the number of ways is C(8, 4) = 70.
Step 3: Calculate the probability by dividing the number of favorable outcomes (selecting all rotten oranges) by the total number of possible outcomes (selecting any 4 oranges from the remaining 8).
Probability = Number of favorable outcomes / Total number of possible outcomes = 70 / 70 = 1.
Therefore, the probability that all oranges selected are rotten is 1/495, which corresponds to option B.
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Community Answer
One-third of 12 oranges got rotten. If 4 oranges are taken out random...
Total rotten oranges = 12/3 = 4
4 oranges can be selected from 12 oranges in 12C4 ways, and four rotten oranges can be selected as a set in 4C4 ways
Hence, the correct option is (B).
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