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 🤯