A stock trader working for a hedge fund has estimated that the stock

Question

A stock trader working for a hedge fund has estimated that the stock of a certain company has probability 0.4 of increasing in price by at least 5 dollars during a certain trading day and probability 0.1 of increasing in price by at least 10 dollars during the trading day. Based on the trader's estimates, select for  X  and for  Y  the options such that the following statement is most accurate. Make only two selections, one in each column.

If the trader multiplies ____ X ____ by the reciprocal of ____ Y ____, then the result is the probability that the price of the stock will increase by at least 10 dollars during the trading day, given that the price increases by at least 5 dollars during the trading day.

ID: 700222

egmat · Accepted Answer

If you found this question difficult, it could be because of one or more of these reasons:
 
 You are scared of probability questions. 
 The question statement is complex because of the use of variables, usage of at least for two aspects.

This question is in fact packed with learnings that you can apply to several DI questions.

Watch this video and observe the visualization at play at 3:32 mark.

https://www.youtube.com/watch?v=FAkchpxfyHs

Let us know if you have any questions.
Happy Learning!

MartyMurray · Answer

A stock trader working for a hedge fund has estimated that the stock of a certain company has probability 0.4 of increasing in price by at least 5 dollars during a certain trading day and probability 0.1 of increasing in price by at least 10 dollars during the trading day. Based on the trader's estimates, select for X and for Y the options such that the following statement is most accurate. Make only two selections, one in each column.

Here's an intuitive way to answer this question.

Whenever the price increases by $10, it has also increased by $5. So, the price increases by $10 a fraction of the time it increases by $5.

Looking at the information given, we see that the price increases by $10 on 0.1 of the time, and the price increases by $5 0.4 of the time.

Accordingly, the price increases by $10 0.1/0.4 = 1/4 of the time it increases by $5.

So, given that the price has increased by $5, the probability that it will increase by $10 is 1/4.

Now, we need a way to express 1/4 using the statement and answer choices.

The statement says the following:

If the trader multiplies ____X____ by the reciprocal of ____Y____, then the result is the probability that the price of the stock will increase by at least 10 dollars during the trading day, given that the price increases by at least 5 dollars during the trading day.

So, we have the following:

the probability that the price will increase by at least 10 dollars given that the price increases by at least 5 dollars = 1/4 = X * the reciprocal of Y

So, we need to find answer choices for X and Y such that 1/4 = X * the reciprocal of Y.

0.1

0.4

0.1 divided by 0.4

the reciprocal of 0.1

the product of 0.1 and 0.4

We see that the two choices for for X and Y such that 1/4 = X * the reciprocal of Y are 0.1 for X and 0.4 for Y, as we can see from the following:

0.1 * 1/0.4 = 0.1/0.4 = 1/4

Correct answer:  0.1, 0.4

chetan2u · Answer

At least 5 dollars would include at least 10 dollars too. So, if increase by at least 5 is 4 times out of 10 times and increase by at least 10 is 1 times out of 10 times, then every time the price goes up by 5 dollars, there is a certain probability that it will go above 10 too.

Thus, we take increase by at least 5 dollars as the total outcome and increase by at least 10 dollars as the favourable outcome.
P(at least 10 given price has increased by 5) =  \frac{0.1}{0.4}

This is 0.1 multiplied by 1/0.4 or 0.1 multiplied by reciprocal of 0.4

Answer given is wrong and being edited accordingly.

KarishmaB · Answer

Reading the first sentence of the question, I was reminded of conditional probability. Note that P(Increase in price by at least 10 dollars) is a subset of P(Increase in price by at least 5 dollars).

Say if there are 15 days when the price increased by at least 5 dollars, some of these days would form the set in which the price increased by 10 dollars. Hence, P("At least $5 increase" AND "Atleast $10 increase") = P(At least $10 increase)

We need to find:  probability that the price of the stock will increase by at least 10 dollars during the trading day, given that the price increases by at least 5 dollars during the trading day.  Then

P("At least $10 increase" given "At least $5 increase") is simply P(At least $10 increase) / P(At least $5 increase) = 0.1/0.4

Hence, if the trader multiplies 0.1 (ANSWER) by the reciprocal of (0.4) (ANSWER), then we will get 0.1 * (1/0.4) = 0.1/0.4 (this probability)

Check out my discussion on conditional probability through the Super Sunday program (details below in my signature) or  click here :  https://youtu.be/gN_vlDpUflo

Danny134 · Answer

How can we solve it via conditional probability?

ruis · Answer

Official answer with conditional probability https://gmatclub.com/forum/download/file.php?id=82191 GMAT-Club-Forum-2tc65lwj.png

mayankdgmat · Answer

I have done this in following way:

It is given that price has increased by at least 5.

Suppose there are 10 outcomes possible, as per the probability in 4 instance stock will increase by at least 5.

So now we have 4 cases available with us since it is given to us that one of the case has already happen

in same 10 outcomes, at least 10 has 1 favorable instance. So out of remaining 4, 1 is favorable hence answer is 1/4

Gemmie · Answer

To find the correct values for X and Y, we need to determine the conditional probability that the price of the stock will increase by at least 10 dollars given that it increases by at least 5 dollars.The conditional probability formula is:

1. The probability of the stock increasing by at least 5 dollars is 0.4.
2. The probability of the stock increasing by at least 10 dollars is 0.1.

If we know the stock has already increased by at least $5, we are looking at a subset of days when the price increased by at least $5.

Among these days, we want to find the fraction of days when the price increased by at least $10 (which are all included in this at-least-$5 subset).

To get this fraction, we take the probability of a $10 increase (0.1) and compare it to the probability of a $5 increase (0.4). This comparison is done by dividing 0.1 by 0.4.

=> Probability =  \frac{0.1}{0.4} = 0.1 * \frac{1}{0.4}

Thus, the correct choices are:

X = 0.1
Y = 0.4

---
 To put it in a simpler way:
We have 10 stocks
=> 4 increases at least $5
=> 1 increase at least $1

Among $5-increase stock, the probability of $1-increase stock is 
 \frac{1}{4} = \frac{0.1}{0.4} = 0.1 * \frac{1}{0.4}

Kianadunn · Answer

Let's break down the problem step by step. The trader estimates a 0.4 probability that the stock will increase by at least $5, and a 0.1 probability that it will increase by at least $10. To find the probability that the stock increases by at least X dollars but less than Y dollars, we calculate the difference between these probabilities.

SirSanguine · Answer

P(Event E Given that F) = P ( E and F)/ P(F)

P(E|F)=P(E n F)/P(f)

PeachSnapple1 · Answer

Love this question, as it really tests how you approach probability. Even if one doesn't know the Bayes's Theorem, one could still solve it. 
The question asks  given that the price increases by at least 5 dollars during the trading day. ] Now, if the question doesn't have the bold and underlined part, the answer would be 0.1 according to the prompt.

But the probably only tricky thing here is that, now we know for sure that trading day will increase by at least 5 dollars, our denominator becomes 0.4. So the P(trade at least $10 given that the day trading has already been at least $5) = 0.1/0.4 = 1/4
The only difference between conditional probability, P(A given B), and P(A) is their denominators, while the numerator stays the same, which P(A).

ManifestDreamMBA · Answer

Solved it using P(B|A) = P (A and B)/P(A)

Probability of increasing in price by at least 5 dollars, A
P(A) = 0.4

Probability of increasing in price by at least 10 dollars, B
Note, this will happen only when Probability of increasing in price by at least 5 dollars, A is achieved
P(A and B) = P(B) = 0.1

P(B|A) = 0.1/0.4 OR 0.1 * 1/0.4

X = 0.1 and Y = 0.4

agrasan · Answer

There are already amazing explanations above but if we want to solve this question using conditional probability formula.
Event A = stock price is at least $10
Event B = stock price is at least $5

When we say P(A|B), it is probability of event A happening when event B has already happened

P(A|B) = P(A and B)/P(B)

Now,  A and B  refers to intersection of events A and B and if you visualize a number line then  A and B  is stock price at least $10

P(stock price is at least $10 given it is at least $5) = P(stock price at least $10) / P(stock price at least $5)
P(stock price is at least $10 given it is at least $5) = 0.1 / 0.4 = 25%

A stock trader working for a hedge fund has estimated that the stock

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A stock trader working for a hedge fund has estimated that the stock