Math problem for Day 2 on D.Buzz for March 2021 😎

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Math problem for Day 2 😎

In a contest, Ahmad (A) must guess where the hidden prize is in 10 baskets to win. After A guessed, the host removed 5 empty baskets and offered A the chance to switch baskets. If A has a 70% chance of switching, what is the probability that he wins?

math mathematics minicontest dbuzz contest baskets probability
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It's late and going to sleep soon so just the answer that came to me first: 17.2%.

Work in following comment.

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If no switch: 20% = 0.2

If switch, I assume it is just one basket swapped: 20% for correct one swapped.
0.20 + 0.24 = 0.16

Total = 0.3(0.2) + 0.7(0.16)= 0.172 = 17.2%

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17%. Monty Hall, hooray. The first guess is 0.1 (1in10) chance, the second 0.2 (1in5). Then distribute the conditional probability: 0.3or30% chance to stay with the first guess plus a 70% chance of switching. (0.10.3)+(0.20.7)

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Ugh, markdown ate my asterisks.
(0.1 x 0.3) + (0.2 * 0.7) = 0.03 + 0.14 = 0.17 = 17%

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A 1 out of 5 (20%) chance to win? I don't think the probability of switching affect the probability of winning, after all if A choose wrong, he'll just switch, we're only talking about the final result, right?

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20% seems to be a too simplified way of determining what Ahmad's (is it you? 😆) chance to win the contest.

It will not make sense to give Ahmad 70% chance to switch baskets if he finds out that the basket does not contain the prize, since a contestant who wants to win will always take opportunity to get the (best) prize. 🤔

Anyway, it does not matter if how many times he makes guesses or switches, as long as the basket is not yet opened. 🙂

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Ah wait, that was me? didn't think of this, yeah it doesn't make sense to be told that those baskets don't contain the prize which is what I assumed...

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(Edited)

Answer for Day 2 Math Problem

18.75% 🎯

Solution

There is a 10% chance that Ahmad chooses the basket with the hidden prize. After that, there can be 4 outcomes, which are the following:

  • Ahmad picks the basket with the hidden prize, and does not switch baskets.
  • Ahmad picks the basket with the hidden prize, but switches baskets.
  • Ahmad picks a basket without the prize, and switches baskets.
  • Ahmad picks a basket without the prize, but does not switch baskets.

We now have the following:

  • The chance to pick the basket with the hidden prize is 10%. After the host removes 5 empty baskets, there is a 30% chance Ahmad does not switch baskets and therefore wins the prize. This outcome has a 10% * 30% = 3% chance of occurring.
  • The chance to pick a basket without the hidden prize is 90%. After the host removes 5 empty baskets, there is a 70% chance Ahmad switches baskets. Ahmad has 25% chance of having picked the winning basket after he switched, since there are only 4 remaining baskets remaining and one of them has the hidden prize. This outcome has a 90% * 70% * 25% = 15.75% chance of occurring.

The chances of Ahmad picking the basket at the end of the contest is 3% + 15.75% = 18.75%.

Anyway, it does not matter how many times Ahmad actually picks a basket or switches baskets, as long as the basket is not opened to reveal if the prize is inside. 🙂

Winner: none 🤯

The 1 HIVE prize for today is reserved for the next day there is a winner. 🏧 The 1 HIVE prize reserved from Day 1 will also be added, so the winner for the next day will win a total of 3 HIVE! 🤑😆

  • I am confused about @jfang003's solution. 🤯 Sorry! 😅
  • @eturnerx-dbuzz just forgot to multiply the scenario in which Ahmad does not pick the basket with the prize the first time by 90% or 0.9. He was so close! 😅

Mentions: @holovision, @ahmadmanga (@ahmadmangazap), @minus-pi, @dkmathstats, @paultactico2, @appukuttan66
Special mentions: @dbuzz, @chrisrice, @jancharlest, and @mehmetfix 🤯

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Thank you for private labeling.
Unfortunately, I am not interested in mathematics. And of course I'm not interested in physics
In the Electronic Technology Program, we also see courses such as physics and I do not understand much. :(

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What is "private labeling"? 🤔 Anyway, since you said you are not interested in mathematics, I will no longer tag you from now on. 🙁

Physics (especially mathematics) can never be taken away from Electronics courses. I assume you have thought about that before pursuing an Electronics degree. 😐

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(Edited)

I mean Special Mention 😂

I'm not interested in math and physics. But I didn't say this so that you wouldn't mention me. You can tag me whenever you want. No problem. This is a very good thing for me. @savvyplayer 🤗

I attended the electronic technology program not for theoretical courses but for practical courses. So as the university department. But because of the epidemic, we only get theoretical lessons.

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Well, it is hard to understand the theory without somewhat good grasp of Math/physics.

Does your college/university allow you to graduate without understanding the theory part? (Assuming there's no pandemic problem of course~)

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I can understand a little of course. 😅
In college, it is a must to take over 50 points from the 2 exams. I usually get around 60 points. In this way, I can pass the lesson 🤭
But I had to take it again because I did not pass the last theoretical course. That is why the number of courses I took this semester is many.

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Pretty sure "private labeling" is another way to say tag/mention...

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There is no "private" (labeling or tagging) on Hive. 🤔🤔

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Yeah there isn't... There is Private Messaging though, (using Encrypted Memos) D.Buzz team is making an interface to streamline that.

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Encrypted memos are no longer "labeling or tagging". 😐

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Do you mean Hive.PM? 🤔

Have some !LUV for helping promote engagement on D.Buzz since a year ago! 😁

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...? This was a year ago, right? I can't read the mind of "me" of a year ago, but I think yes, that's what he meant.

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You don't have to "read" the mind of "you" of a year ago - you just have to recall it! 😆😅

Have some !LOLZ! 😁

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!LOLZ, it depends, sometimes it's easier to read it than recall it.~ Thanks for promoting engagement on my engagement.~

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I think your math is bit wrong. The question itself says that 5 baskets are removed regardless. This means if the basket is not switched then that outcome is 20% * 30% = 6%.

As for the 2nd part, my solution assumed Ahmad switched 1 basket at most and I guess the markdown messed up my work.

20% * 0% for Ahmad changing out the prize basket
80% * 20% = 16% for Ahmad changing out an empty basket with another empty basket. Chances of picking the right basket afterward is 20%.
So 70% * 16% = 11.2%

This means the total percentage is 6% + 11.2% = 17.2%

I think the only thing I did not get correct is the fact that Ahmad might of picked the correct basket first and thus I had zero percent in that case.

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I realized that I was a bit wrong with my solution and answer. Since the host removed 5 empty baskets, assuming Ahmad picked an empty basket and switches, he has a 25% chance (not 20%) to pick the basket with the prize. Thanks for pointing that out! 😅

Anyway, I am still confused with your solution. Sorry again! 🤯

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It was the same as yours for the most part with just a few adjustments. I kind of made a few assumptions. Don't worry about not understanding it.

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