If the probability of Ronaldo will do at least 3 goals in the match is

Question

3 deadly mistakes you must avoid in Probability - Exercise Question #4

4-  -If the probability that Ronaldo will score at least 3 goals in the match is 0.59 and the probability that Ronaldo’s team will win the match is 0.73. What is the greatest probability that neither of the two events will occur.

Options

a)  0.1107
 b)  0.27
 c)  0.41
 d)  0.5693
 e)  0.62

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EgmatQuantExpert · Answer

Solution

Given:

• P(Ronaldo makes at least 3 goals)= 0.59
• P(Ronaldo’s team mins the match)= 0.73

To find:  
 • The greatest probability such that Ronaldo cannot make at least 3 goals in the match and his team could not win the match.

Approach and Working:

Since a team can win a match or not is directly dependent on the number of goals a player will make.
 • Hence, this is a question of dependent probability.
 
The easiest way to solve the problem is by overlapping of sets of two events.
 • If we represent the probability that Ronaldo’s team will win a match by a set, then the circle that represents the probability such that Ronaldo’s team will not win the match= 0.27.
• Now, overlapping the set of occurrences of Ronaldo’s hitting 3 goals and his team winning the match will give the maximum probability of remaining set= 0.27

Hence, the correct answer is option B.

Answer: B

kaushiksamrat · Answer

Answer is a - 0.1107 as probability for not scoring atleast 3 goals is 0.41 and probability for not wining match is 0.27.. so 0.41 X 0.27 = 0.1107

Sent from my SM-G935F using  GMAT Club Forum mobile app

D3N0 · Answer

I think there is an Error. 
Ans A:
Neither of the two event will occur = Probability= .27*.41 = .1107

EgmatQuantExpert · Answer

Hey, It's a trick question actually.

There is no mistake in it. I would request you to go through the following article and read Probability in Dependent Events to understand this question. 3 deadly mistakes you must avoid in Probability There is a similar question asked in GMATPrep, here is the link : Click Here

EgmatQuantExpert · Answer

Hey, Unfortunately your answer is not correct.

I would request you to go through the following article and read Probability in Dependent Events to understand this question. 3 deadly mistakes you must avoid in Probability There is a similar question asked in GMATPrep, here is the link : Click Here

pushpitkc · Answer

Since the event that Ronaldo will score atleast 3 goals in the match and Ronaldo's team
winning the match are dependant, in order to find the greatest probability that neither 
of the events occur, we need to find the individual probabilies:

P(Ronaldo doesn't score 3 goals) = 1 - P(Ronaldo scores 3 goals) = 1 - 0.59 = 0.41
P(Ronaldo's team doesn't win the match) = 1 - P(Ronaldo's team wins) = 1 - 0.73 = 0.27

Therefore, the greatest probability that neither of the events take place is 0.27  (Option B)

P.S Here, the greatest probability that neither of the events will occur is the probability
of the more probable event(Ronaldo's team winning the match) not occuring.

D3N0 · Answer

Please clarify how you reached to this conclusion ? I am still not able to understand this. because if Neither of the event will occur means, as i understand, neither of these two event occur together.. I am really confused with this language of the question.

srinjoy1990 · Answer

P(R3) = Ronaldo scores 3+ = 0.59
P(T) = Team wins = 0.73.

To find Max  =Max

Now, P(R3+T) = P(R3)+P(T)-P(R3T) = 1.32 - P(R3T)
P(R3+T)' = P(R3T) - 0.32.

Now comes the trick, since they are dependent events P(AB)<= min  . This is a standard relation of probability for dependent events. If you want clarification just draw the 2 sets. Since P(AB) is the common region it cannot exceed the minimum of P(A), P(B)  .

So, Max  = 0.59 (Team wins) - 0.32 = 0.27.

This a very good question.

EgmatQuantExpert · Answer

Hey, This question is actually a tricky question. This is a question of dependent probability - When the occurrence or non-occurrence of one event depends on another event. For example: If the price of raw material decreases then the product becomes cheap, right??? Thus, both the events are dependent on each other. And we have thoroughly explained how to avoid the error in the case of dependent event in the article- 3 deadly mistakes you must avoid in Probability . Hope it helps.

Regards, Ashutosh

EgmatQuantExpert · Answer

Hey everyone,

The official answer to the question has been posted.

Regards,
Ashutosh

sssong · Answer

Thank you for the explanation. I thought Ronaldo can make at least 3 goals and a team can still lose a match, or win a match even if Ronaldo makes less than 3 goals, and misunderstood that this is the question of independent probability..

robinbjoern · Answer

I get your point but I think the question is flawed because in essence the events are not dependent. Ronaldo could also score 500 goals if the other teams scores 1 more Ronaldos Team would loose. Also another Team member other than Ronaldo could lead the team to a win. How are we supposed to know that those events are dependent?

josenetofaria · Answer

Hi,
I got your point and it is really a little the meaning regarding what the question is asking is subtle.

Actually, what you said makes sense: the team can win, having Ronald marked >= 3 goals or <3. Or even vice versa, rigth?
I agree with you. 
They are indepedent if you think about one of them independently, as the other doesn't exist.

But, what would you say if you were asked "what are the odds of Ronald marks three or more goals and the team wins?"

In this case, you've changed the scenario, you have a new scenario. The scenarios (goals of Ronald and team win) now are coexisting and can have intersections!
For the sake of illustration, we can have now the following outcomes:

Ronald scores 3 or more goals AND Team wins
Ronald scores 3 or more goals AND Team loses
Ronald scores less than 3 goals AND Team wins
Ronald scores less than 3 goals AND Team loses

Well, what I mean by this is that in a given scenario when we have two or more events (let's say A, B, C,...), they are called Dependent Events when they have intersection (not empty, of course) with each other. And when they don't have any intersection, they are called independent.

Regor60 · Answer

Some of these explanations seem apt to confuse.

It's not necessary to know whether the events are dependent or independent.

The question itself, asking for the maximum, forces the consideration of dependence because that is the scenario that generates the maximum result.

Independent events, X*Y vs min  for dependent.

X*Y is always less than min  when X,Y<1.

Posted from my mobile device

dhairya18 · Answer

Imagine a season of 100 matches total.

In 73 matches, the team wins.
In 59 matches, Ronaldo scores 3 goals.

Now, think about what "neither event happens" means: the team loses AND Ronaldo does not score 3 goals.
Because the team wins in 73 matches, there are only 27 matches left where the team loses (100 - 73 = 27). In those 73 winning matches, "neither happens" is already impossible because the team won. Therefore, the absolute maximum number of matches where neither event happens is 27 out of 100 (0.27).
This maximum occurs if all 59 of Ronaldo's scoring games happen inside the 73 winning games.

Explaining the Options One by One

Option A (0.1107)
What it calculates: 0.41 times 0.27 = 0.1107.
Why it is wrong: This assumes the two events are like flipping two completely unrelated coins (independent). In real life and probability bounds, Ronaldo scoring goals helps his team win. Multiplying gives the probability for independent events, not the greatest possible probability.

Option B (0.27)
What it calculates: 1 - 0.73 = 0.27 (or 27 out of 100 matches).
Why it is correct: Since 73 matches are wins, at most 27 matches are available where a win did not happen. If Ronaldo also failed to score in those same 27 matches, you get the maximum possible value for neither event occurring.

Option C (0.41)
What it calculates: 1 - 0.59 = 0.41 (the chance Ronaldo does not score 3 goals).
Why it is wrong: This completely forgets about the team winning. It only tells you how often Ronaldo fails to score 3 goals, ignoring whether his team won those matches.

Option D (0.5693)
What it calculates: 1 - (0.59 times 0.73) = 0.5693.
Why it is wrong: This calculates the chance that at least one event fails to happen if they were independent. It answers the wrong question entirely.

Option E (0.62)
What it calculates: A random distractor number.
Why it is wrong: It is mathematically impossible because the team already wins in 73% of matches, leaving only 27% where neither could possibly occur.

If the probability of Ronaldo will do at least 3 goals in the match is

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