7 Validación
7.2 Resultados obtenidos
The probability of Tom scoring 40 or over is greater than the probability of Salah scoring 15. The answer is B.
Answers and Explanations
Question 8 - A
We need to list the different combinations which will give us a cumulative score of 16 or more.
• 3 six
• 2 six + 1 five • 1 six + 2 five • 2 six + 1 four
We do not need to write out everything for the last two combinations of 1 six / 2 five and 2 six / 1 four, as they will have the same probability as 2 six / 1 five.
The probability of getting any combination is 1/6 x 1/6 x 1/6 = 1/216 • The probability of getting 3 sixes is 1/216 as there is 1 combination.
• The probability of getting 2 sixes and 1 five is 3/216 as there are 3 combinations. • The probability of getting 1 six and 2 fives is 3/216 as there are 3 combinations. • The probability of getting 2 sixes and 1 four is 3/216 as there are 3 combinations. The total probability of getting 16 or more = (1 + 3 + 3 + 3) / 216 = 10 / 216
The answer is therefore A.
Roll 1 Roll 2 Roll 3
3 six 6 6 6 2 six + 1 five 6 6 5 6 5 6 5 6 6 Continued…
Answers and Explanations
Question 9a - D
For Amaru to pick Chile, it has to be avoided by the first two picks of the draw. • The probability of not picking Chile in the first round is 6/7.
• The probability of then not picking Chile in the second round is 5/6. • The probability of then picking Chile in the third round is 1/5. All of these three events need to happen for Amaru to pick out Chile. P (Amaru picking Chile) = 6/7 x 5/6 x 1/5 = 30/210 = 1/7 = D
Question 9b - C
For this to happen we need two South American teams drawn in the first two picks, and a European team in the third pick.
The table below shows all the combinations possible:
The probability of any given combination is 1/7 x 1/6 x 4/5 = 4 / 210 = 2 / 105
There are 6 combinations, so the probability of Amary picking the first European time is 6 x 2 / 105 = 12 / 105.
Medic Mind Tip: Above we have gone through the longer method to show clearly the
different combinations. However, you know the probability of picking a South American team first is 3/7, and then second is 2/6, and then picking a European team third is 4/5. So
Team 1 Team 2 Team 3
Brazil Argentina European
Argentina Brazil European
Brazil Chile European
Chile Brazil European
Chile Argentina European
Argentina Chile European
Answers and Explanations
Question 10 - D
This is an example of Pattern 12 of Medic Mind’s Guide to Syllogisms. • A is not showing that no windows are satellites.
• B is showing that some windows are satellites, which is false. • C is showing that no chairs are satellites.
• D is the correct answer. It shows that all windows are chairs, but no windows are satellites.
Question 11 - C
Probability of Event = Probability of rolling 6 x Probability of flipping a head
Probability of Event = 1 / 6 x 1 / 2 = 1/12 There are 7 days x 6 weeks = 42 repeats of the event.
Expected Frequency = Probability x Number of Repeats
Expected Frequency = 1/12 x 42 = 3.5 days You can’t have 3 and a half times, so the answer will be 3 = C.
Question 12 - D
P (She pops the red balloon) = P (She pops the red first) + P (She pops the red second) In the previous question we mentioned that we took the long route in the explanation by breaking down all the possible combinations. Here we are going to go straight for the short route, as hopefully you are comfortable with probabilistic reasoning questions by now. P (She pops the red first) = 1/3
P (She pops the red second) = 2/3 x 1/2 = 2/6
For the second calculation, we multiply the probability she pops a non-red first (2/3) by the probability she pops the red next (1/2) out of the two balloons remaining.
P (She pops the red balloon) = 1/3 + 2/6 = 4/6 = 2/3
Answers and Explanations
Question 13 - C
Looking at the question, we need to look for areas of overlap. The easiest ones to rule out are the ones that involve the fewest categories. Let’s start with A. Scuba diving is a
pentagon, and there is an area in the pentagon that is not overlapping with other regions. We can therefore rule A out, as scuba diving is available as a sole activity.
Next look at the answers with two categories. B and C fit this description. We need to look for an overlap of a pentagon and diamond for B, and we see that so B can be ruled out. We need to look for an overlap of a diamond and an arrowhead for C - these two do not overlap, therefore C is the correct answer.
Question 14 - B
• A is not a valid reason for the UK to also have military service. Just because one country is doing it, it does not mean it is successful. The statement also does not address how it will affect future careers.
• B is the correct answer as it gives examples of how the military service could help someone gain skills.
• C is a good reason, but it does not focus on how it will affect 18 year olds careers, but instead focuses on how it will influence the economy.
• D is an assumption based on a lack of evidence.
Question 15 - C
As we learnt in Tutorial 4: Venn Diagrams, when you get this type of Implicit Text to Venn question, they will not explicitly tell you to draw a Venn Diagram. However, you have to draw one to answer the question.
As always, we start with the information involving the most categories. 3 people had all orange juice, lemonade, banana smoothie…
Answers and Explanations
18 people had banana smoothie and orange juice… 50 people had banana smoothie…
The overlap between Orange and Banana smoothies includes 15 + 3 = 18. The overlap between Lemonade and Banana smoothies includes 24 + 3 = 27.
Orange Lemonade Banana Smoothie 3 Orange Lemonade Banana Smoothie 3 24 15
Answers and Explanations
50 people had banana smoothie…
20 people had orange juice as their only drink… 4 people had lemonade as their only drink…
The Banana smoothie circle in total contains 50 people. We did 50 - 15 - 3 - 24 = 8 to get the value for the ‘Banana only’ region.
The Orange circle has 20 people in the ‘Orange only’ region. The Lemonade circle has 4 people in the ‘Lemonade only’ region.
47 people had orange juice… 40 people had lemonade…
Orange Lemonade Banana Smoothie 3 24 15 20 8 Orange Lemonade Banana Smoothie 3 24 15 20 8 x
Answers and Explanations
We came to this information last because before this point we had two or more unknown regions for both Orange and Lemonade, so we needed to fill regions up before using this data.
Orange Juice 20 + 15 + 3 + x = 47 x = 9
You could have also used the lemonade value of 40 to do a similar calculation.
Therefore the total number of people who had both orange juice and lemonade is 3 + 9 = 1
Question 16 - A
This is an example of a Text to Venn question, the first type of question we learnt in the Venn Diagrams tutorial.
1. Whenever you get a Text to Venn question such as this, a good thing to check would be that the Venn adds up to the total mentioned in the question text.
There were 34 participants…
When counting up the numbers for each Venn diagram we find: A - 34
B - 34 C - 35 D - 34
This means we can rule out C
2. Now, as always first use the information that tells us about the most categories.
11 people use all three…
Looking at all four options, all have 3 in the middle except B. This means we can rule out B
Answers and Explanations
3. Next we look at information that tells us about 2 categories
6 people use two forms of transport…
Unfortunately, this does not help us as A and D both have a 6 in between two circles!
4. Normally, we would now look at information that tells us about 1 category, but we are given an extra piece of information
The same number of people that use bus only as Tube only...
This means that at the centre of each circle there should be two numbers that are the same.
A - Yes D - No
This rules out D
This means the answer is A.
Question 17 - C
For this type of question we cannot do much from just the Venn, apart from set up the formula:
13 + 2X + 2Y + 11 + 24 = 60 so… 2X + 2Y = 12 It is better to now go through each statement:
A. Let us investigate:
The number of people with 2 options is 2X + 11. The number of people with 1 option is 27 + 2Y
Using the equation above (2X + 2Y = 12), we can substitute 2X with 12 - 2Y:
Answers and Explanations
The number of people with 1 option is 27 + 2Y
Therefore the number of people with 1 option is greater.
B. This is false, as there are no people with all four options because there is no overlapping region covering all four sets. We can calculate it - it is zero!
C. Let us investigate:
The number of people with fries = X + Y + 11 The number of people with apple pie = X + Y
By inspection we can see that 11 more people had fries than apple pie.
D. For completion sake, let us investigate:
The number of people with pizza = X + 13 The number of people with watermelon = X + 35
By inspection we can see that 22 more people had watermelon than pizza.
Question 18 - C
This is a Euler diagram question. These are different to Venn diagrams, because they represent real-life relationships between categories. Here we are given information about Geography, and are told that one of the four diagrams represents the information.
We know that England, Scotland and Wales are three different countries. They all come under Great Britain and Great Britain comes under the United Kingdom (along with Northern Ireland).
We are therefore looking for one circle enclosed in another circle which contains three smaller circles. The answer is therefore C.
Answers and Explanations
Question 19 - C
A. No. There could have been some under 30 years older that were right handed, it was just that none of the winners fit the category of being left-handed and older than 30 years old.
B. No. We do not have sufficient information to make this assumption. C. Yes. This is true - the information tells us this.
D. No. We only know that none fit into the category of being left-handed and older than 30 years old. The winners could have been either right handed and over 30 years old or younger than 30 years old and left or right handed. This means that we do not know if all the champions in the past three years younger than 30 years are left handed, as we don’t know if they were all younger than 30 years.