Probability Help!!

Question

Hi Guys,

I came across the below problem in an online practice test..I wanted to check if my approach is rite?

There are 5 monkeys on an island. Each monkey has a boat. Each monkey take his boat and tries to get off the island. If the probability of each boat sinking is 1/4, what is the probability that all monkeys make it safely back except for King Kong who took the S.S. Banana, approximately?

Here's my aprroach:

P(boat sinking) = 1/4
P(boat not sinking) = 1-1/4 = 3/4

P(all monkeys make it safely except kingkong) = 3/4*3/4*3/4*3/4*1/4 = 81/1024.

After solving the problem, i had a second thought because the question asks for what is the probability that all monkeys make it safely ..
so would it just be:

P(all monkeys make it safely except kingkong) = 3/4*3/4*3/4*3/4= 81/256.

any suggestions pls?

Regards,
Anu

amit2k9 · Answer

King Kong's boat is redundant and assuming SS boats probability of reaching safely as 1, we have the following --

The probability has been asked for reaching of all the monkeys safely means (3/4) ^4 * 1.

I hope if you mention the options it will be easier to take a better STAB at this.

fluke · Answer

The question is asking you to deduce the probability of 4 monkeys reaching ashore safely AND a must sinking of King Kong's boat. You can't count King Kong out because you have to take care of sinking him.

I believe the former method holds good;
P(all monkeys make it safely except kingkong) = 3/4*3/4*3/4*3/4*1/4 = 81/1024.

retro · Answer

To take Fluke's explanation a step further, I'd actually think that the probability that at least one of them sinks is 1 1 - P(All boats making it safely back to the bank). AM I right?

The special monkey mentioned in the question has not been attributed any different probability data. So I'd guess he should be treated is as normal as others are treated when solving the question.

Regards
Rahul

anuu · Answer

@ Director..The answer choices mentioned are:

1/5 , 81/1024 , 1/4 , 81/256 and 3/5.

The source for the question is : https://gmat.jumbotests.com/tests/gmat-p ... -test-math

question number 33 of 37.

Regards,
anu

seoulite · Answer

If you're implying that King Kong is not one of the monkeys, and you need to find the probability that all 5 monkeys make it back safely then the answer should be (3/4)^5 = 243/1024.

If King Kong is one of the monkeys then your original answer is right (3/4)^4 * 1/4 = 81/1024. At least that's the way I interpreted the question.

daijy1234 · Answer

Hi, you are in fact right. The probability of  at least  1 sinking is = 1 - P(none sinking).

You are also correct in stating that the special monkey mentioned isn't attributed to any different probability data. Each monkey has a 1/4 chance of sinking and a 3/4 chance of making across without sinking. Also, each monkey's chances are independent of one another so each is an independent scenario, so to speak. The answer should be (3/4)^3 * (1/4) = 81/1024

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