SIG Quantitative Evaluation Practice Test
A faulty chat-bot is known to get any random maths question right 65% of the time. If you ask the chat-bot 15 questions, what are the odds that it gets exactly 10 right? Express your answer as a decimal rounded to 2 decimal places.
In a realm of wizards (who always tell the truth) and sorcerers (who always lie), two individuals, P and Q, make statements: P says, 'Q is a Wizard', to which Q responds with 'P is a Wizard'. What are P and Q?
There are 13 people at a birthday party that have a 35% chance of eating no cake, a 60% chance of eating a tenth of the cake, and 5% of eating a fifth of the cake. Is the cake expected to be completely eaten?
A bag contains 5 pencils, 3 erasers, and 2 sharpeners. If 3 items are drawn at random without replacement, what is the probability that all 3 items drawn are all different objects? Express your answer as a decimal rounded to 2 decimal places.
You flip 3 coins. What are the odds you get exactly 1 tails or exactly 1 heads? Express your answer as a decimal rounded to 2 decimal places if needed.
You are playing roulette at a low budget, run down casino. You notice that the roulette wheel is ever so slightly slanted down toward the 17, giving it a 1% more unit chance of it hitting. It pays 35x profit from your betting wager if it hits. If the previous odds of the 17 hitting was 1/38, are you expected to profit, lose, or approximately stay the same wealth if you employ this strategy and continuously bet on 17?
True or False: if all athletes train hard, and some trainers are athletes, then some trainers train hard.
A bag contains 6 red balls and 4 blue balls. Two balls are drawn sequentially without replacement. What is the probability that both balls are of the same color? Express your answer as a decimal rounded to 2 decimal places if needed.
A car travels from Town A to Town B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the entire round trip in km/h? Round your answer to 2 decimal places if needed.
At a tech startup, if a software update is successful today, there's an 80% chance the next update will be successful. If today's update fails, there's a 70% chance the next update will succeed. Assuming the first update is successful, how many updates, to the nearest update, will be successful out of 150 updates?
Consider a 50 sided fair die. If you roll the dice 14 times, find the expected value from the set of numbers which are divisible by 9. Round your answer to 2 decimal places if needed.
Two friends are playing a game where each chooses a sequence of heads (H) or tails (T) of length 3. The sequence that appears first in a series of coin flips wins. Given friend A chooses 'HHH', what sequence should friend B choose to maximize their chances of winning?
In a survey, 20% of respondents own a dog. Among dog owners, 95% prefer to walk their dogs in the evening. Among non-dog owners, 10% prefer to take evening walks. If a person prefers evening walks, what is the probability that they own a dog? Express your answer as a decimal rounded to 2 decimal places.
Six colleagues (Ben, Jack, Blake, Sophia, Ulysses, and Claire) are seated in a row for a meeting. Jack is not next to Ben, Blake is not next to Sophia, Ulysses is not next to Jack, and Ulysses is to the left of Blake. Based on these conditions, who is seated to the left of Jack?
You want to build a rectangular enclosure with a fixed perimeter of 80 meters. What is the maximum area? Round your answer to the nearest square meter.
A diagnostic test for a certain disease is known to correctly identify the disease in 99% of cases where a person has it, and to incorrectly identify the disease in 3% of cases where the person does not have it. If 1% of the population has this disease, what is the probability that a person actually has the disease given that the test results are positive?