Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

A Quiz With Two Questions

Janet is going to take a quiz with only 2 questions.

Here are the two questions:

1. NYC is located in Egypt. True or False.

2. The deep end of a swimming pool is the same as the shallow section. True or False.

What is the probability if Janet choses TRUE or FALSE at random?

Let me see.

There are only two choices for each question. So, the probability that Janet will select True for question 1 is 1/2.

The probability that Janet will select False foe question 2 is also 1/2.

Janet's selection for question 1 does not effect her selection for question 2.

I say this question is an example of independent events.

Let A = selecting True for question 1.

Let B = selecting False for question 2.

I need P(A and B) = P(A) • P(B).

P(A and B) = (1/2) (1/2) = 1/4.

You say?

Last edited by mathxyz (2024-05-12 06:06:24)

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 248

Re: A Quiz With Two Questions

Well done, I couldn't do it better.

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 61

Re: A Quiz With Two Questions

Edit: Originally it wasn't specified that the answers were chosen at random.

Original post:
I think it's common knowledge that NYC is not in Egypt and that the deep end of a swimming pool is not the same as the shallow end. So it would be quite unlikely for someone to answer (True) and (True); probably less than 5%.

They might not be independent either.

Looks like the question is made to make you think about these things.

But I would suggest P(A) is probably much lower than 1/2, and P(B) much higher than 1/2.

Last edited by Keep_Relentless (2024-05-12 18:38:52)

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"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: A Quiz With Two Questions

Well done, I couldn't do it better.

Thanks. I appreciate the positive words. Look for similar probability problems later today. I will try to post one math topic at a time, which allows for further math discussions.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: A Quiz With Two Questions

It ought to say "If Janet choses TRUE or FALSE at random"

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: A Quiz With Two Questions

It ought to say "If Janet choses TRUE or FALSE at random"

Bob

Thanks. I will edit now.