Question

Considering a survey conducted on a harvest of mangoes, it was discovered that 10% of Alphonso Mangoes and 20% of Hapus Mangoes were found to be rotten inside. If one Alphonso Mangoes and two Hapus Mangoes are randomly chosen from the lot, what is the probability that at least one out of the three mangoes will be rotten inside ? (Round off the answer to 2 decimal places )

Answer 1

The probability that an Alphonso mango is good is 0.9.

The probability that a Hapus mango is good is 0.8.

The probability that one Alphonso AND one Hapus AND another Hapus are all good is:

(0.9)(0.8)(0.8) = 0.576

Therefore the probability that at least one out of the three mangoes will be rotten inside is:

1 - 0.576 = 0.424 or 0.42

Comments

Why the answer can't be 0.784?
I assumed there are 10 rotten Alphonso Mangoes and 90 Good Alphonso. Again, 20 rotten Hapus Mangoes and 80 Good Hapus Mangoes.

Then, I calculated the total number of possible of selecting 3 mangoes out of 200 i.e. (²⁰⁰C3)
Now to calculate the probability that atleast one of them is rotten :
P( At least one of them is rotten) = 1-P(None of them is rotten)

P(None of them is rotten) = (⁹⁰C1)(⁸⁰C2)/(²⁰⁰C3)
Therefore, P(At least one of them is rotten) = 1-[(⁹⁰C1)(⁸⁰C2)/(²⁰⁰C3)]

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Thank you for your comment.
The problem with your reasoning is that you are making the assumption that there are 100 Alphonso Mangoes and 100 Hapus Mangoes.  We cannot make that assumption.  We do not know how many mangoes we have!
To see how your assumption is faulty, try redoing your work assuming that there are 1000 Alphonso Mangoes instead of just 100.  You will get a completely different answer.
No, we use the information we are given. 10% Alphonso and 20% Hapus mangoes are rotten.
I hope this helps.  Please let me know what you think.

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Hey, thanks for your reply. I truly agree with the support argument that you gave.
I need your help in my problems.
How may I contact you?
Any email?