UCAT Decision Making Test #6

Question 1

I pay out £1 to roll two dice. If exactly one die displays a five, I win £2. If exactly two dice produce a five, I win £10.
Should I anticipate making money if I play 36 games?

Accepted Answer

No, since on average I will lose more money than I spend on gambling.

Answer

To determine if playing 36 games is profitable, we calculate the expected value per game. There are 36 possible outcomes when rolling two dice. The probability of exactly one five is 10/36 (winning £2), and exactly two fives is 1/36 (winning £10). The expected winnings per game are (10/36 * £2) + (1/36 * £10) = £30/36 = £5/6. Since the cost to play is £1, the expected loss per game is £1 - £5/6 = £1/6. Therefore, over 36 games, an average loss of £6 is anticipated.

Question 2

Should election voting be done online, or if necessary, by mail, in order to cut expenses, enhance accuracy, and increase turnout?
Choose the one that you think best supports the claims below.

Accepted Answer

No, purchasing the necessary equipment would be expensive, using electronic voting would deter some voters, and there is a chance that hackers may tamper with the outcome.

Answer

The question asks for the best argument regarding online/mail voting to cut expenses, enhance accuracy, and increase turnout. Option D directly counters these claims by highlighting potential downsides. It points out that purchasing necessary equipment would be expensive, electronic voting might deter some voters, and there's a risk of hacking, directly addressing and refuting the proposed benefits of the change.

Question 3

Should the majority of students view university as a time to learn valuable transferrable skills and prepare for life rather than as offering vocational training for a specific job?
From the statements below, pick the one that makes the most sense.

Accepted Answer

Yes, the majority of university courses are designed to prepare students for a variety of possible careers and lives rather than a single employment.

Answer

The question asks whether university should be viewed as preparation for life and transferable skills, rather than specific vocational training. Option C supports this by stating that most university courses are designed to prepare students for a variety of possible careers and lives. This aligns with the idea of developing broad, adaptable skills and knowledge applicable to diverse paths, characteristic of a comprehensive university education.

Question 4

There are equal numbers of people with little feet, medium feet, and giant feet in the nation of Bipodia.
The population is equally split between those who have blue eyes, brown eyes, or green eyes.
Eye color and foot size are unrelated.

Less than 35% of the 100 people drawn at random from Bipodia are predicted to have both blue eyes and small feet.

Accepted Answer

Yes, since foot size and eye color are unrelated and each fraction is one-third, the figure will be around 11.

Answer

If there are equal numbers of people with little, medium, and giant feet, then 1/3 of the population has small feet. Similarly, 1/3 of the population has blue eyes. Since eye color and foot size are unrelated, the probability of having both blue eyes and small feet is the product of their individual probabilities: (1/3) * (1/3) = 1/9. For a random sample of 100 people, (1/9) * 100 = 11.11, meaning around 11 people are predicted to have both blue eyes and small feet, which is less than 35%.

Question 5

Two goods were tested on the market by a corporation.
Users of the products left either favorable or negative feedback.
About 20 out of every 200 customers did not utilize Product A, and 10 out of every 180 people who did gave it poor reviews.
About 90% of the clients used Product B, and 25% of them left favorable reviews.

Is Product A a better product to launch if we simply take into account the likelihood that buyers will utilize and like it?

Accepted Answer

Yes, it is likely that Product A will sell more because there is a bigger chance that buyers will give it favorable reviews.

Answer

To compare the products, we calculate the likelihood of favorable reviews among those who used each product. For Product A, 180 customers used it (200 total - 20 did not use), and 170 gave favorable reviews (180 - 10 poor reviews), resulting in a 170/180 ≈ 94.4% favorable rate. For Product B, 25% of users left favorable reviews. Since Product A has a significantly higher chance of receiving favorable reviews (94.4% vs. 25%), it is the better product to launch based on this criterion.

UCAT Practice Test

UCAT Practice Test

UCAT Decision Making Test #6