Probability Calculations - CCAT Test Prep

This type of question tests your understanding of probabilities, specifically the likelihood that an event will not occur. The scenario provided deals with calculating the probability that two independent events (two flights) will both avoid a certain outcome (being delayed). By understanding how to combine probabilities, you can find the solution easily.

Pasted%20image%2020241011110421

How to Calculate Combined Probability Step-by-Step

Question 1 - Probability Calculation

An analyst determines that on any given flight there is a 20% chance that the flight will be delayed. If this is true and someone takes a round trip (two flights), what are the chances that NEITHER flight will be delayed?

  • A) 56%
  • B) 60%
  • C) 64%
  • D) 70%
  • E) 80%

Step 1: Find the Probability of No Delay for One Flight

  • The probability that a flight will be delayed is 20%.
  • Therefore, the probability that a flight will NOT be delayed is 80%.
Probability of 
no delay for one flight 
	= 100% - 20%
    = 80% (or 0.8)

Step 2: Calculate Probability of No Delay for Two Flights

  • Since the two flights are independent, we multiply the probabilities of each flight having no delay.
Probability of neither flight being delayed
      = 0.8 × 0.8
      = 0.64 (or 64%)

Answer: 64%

This approach allows you to quickly calculate the combined probability without needing complex multiplications.

Question 2 - Probability with Independent Events

There is a 10% chance of rain on each of two consecutive days. What is the probability that it will NOT rain on either day?

  • A) 70%
  • B) 72%
  • C) 80%
  • D) 81%
  • E) 90%

Step 1: Find the Probability of No Rain on One Day

  • The chance of rain on a given day is 10%, so the probability of no rain is 90%:
Probability of 
no rain on one day 
 = 100% - 10%
 = 90% (or 0.9)

Step 2: Calculate Probability of No Rain on Both Days

Probability of 
no rain on both days
      = 0.9 × 0.9
      = 0.81 (or 81%)

Answer: 81%

Question 3 - Multiple Outcomes

A machine has a 25% chance of failure during operation. If the machine is used twice, what is the probability that it will not fail during either operation?

  • A) 45%
  • B) 50%
  • C) 56.25%
  • D) 60%
  • E) 75%

Step 1: Find the Probability of No Failure for One Operation

  • The probability of failure is 25%, so the probability of no failure is 75%:
Probability of 
no failure in one operation 
	= 100% - 25%
    = 75% (or 0.75)

Step 2: Calculate Probability of No Failure in Both Operations

Probability of 
no failure in both operations
      = 0.75 × 0.75
      = 0.5625 (or 56.25%)

Answer: 56.25%

How to Solve These Questions Easily

  1. Identify Probabilities for Each Event: Determine the chance that the event will not occur by subtracting the given probability from 100%.
  2. Multiply for Independent Events: Multiply the probabilities of each independent event to find the overall chance that none of the events happen.
  3. Keep It Simple: Break down each step to avoid confusion and make the calculation easy to handle.

20 Practice Questions - Probability Calculations

  1. If there is a 30% chance that a device will malfunction on any given day, what is the probability that it will not malfunction over two days?
  • A) 40%
  • B) 49%
  • C) 51%
  • D) 70%
  • E) 77%
  1. A team has a 15% chance of losing each match. What is the probability that the team will not lose any of their next two matches?
  • A) 68%
  • B) 72.25%
  • C) 76.5%
  • D) 85%
  • E) 90%
  1. The probability of a software update failing is 5%. What is the probability that two consecutive updates will both succeed?
  • A) 75%
  • B) 81%
  • C) 90.25%
  • D) 95%
  • E) 99.75%
  1. A coin has a 50% chance of landing heads. What is the probability of getting heads on both of two flips?
  • A) 25%
  • B) 30%
  • C) 50%
  • D) 75%
  • E) 80%
  1. There is a 12% chance that a project will be delayed. What is the probability that two consecutive projects will both be on time?
  • A) 66.5%
  • B) 67.2%
  • C) 76.5%
  • D) 77.4%
  • E) 77.44%
  1. A light bulb has a 2% chance of being defective. What is the probability that two bulbs are not defective?
  • A) 90%
  • B) 95%
  • C) 96%
  • D) 96.04%
  • E) 98%
  1. A car has a 10% chance of a breakdown on each of two trips. What is the probability that the car will not break down on either trip?
  • A) 60%
  • B) 70%
  • C) 72%
  • D) 81%
  • E) 82%
  1. A plane has a 5% chance of being late. If two flights are taken, what is the probability that neither is late?
  • A) 80%
  • B) 85%
  • C) 90.25%
  • D) 95%
  • E) 97%
  1. The chance of rain on a day is 25%. What is the chance it will not rain for two days in a row?
  • A) 56%
  • B) 62.25%
  • C) 75%
  • D) 85.75%
  • E) 87%
  1. The chance of a train delay is 20%. What is the probability that two trains will both be on time?
  • A) 40%
  • B) 50%
  • C) 56%
  • D) 64%
  • E) 80%
  1. If there is a 15% chance of rain on a given day, what is the probability it won't rain for three consecutive days?
  • A) 50%
  • B) 60.84%
  • C) 70%
  • D) 73.78%
  • E) 85%
  1. A lamp has a 30% chance of failing during a power surge. What is the probability that it will not fail in two power surges?
  • A) 40.5%
  • B) 48%
  • C) 49%
  • D) 51%
  • E) 72%
  1. A student has an 8% chance of missing a class. What is the probability they attend all of their next three classes?
  • A) 65%
  • B) 72%
  • C) 74.2%
  • D) 77.37%
  • E) 80%
  1. The probability of a power cut in a day is 4%. What is the probability that two consecutive days will be without a power cut?
  • A) 70%
  • B) 78%
  • C) 80%
  • D) 92%
  • E) 96%
  1. The chance that a door lock fails is 3%. What is the chance that two locks do not fail?
  • A) 85%
  • B) 90.7%
  • C) 93%
  • D) 94.09%
  • E) 97%
  1. A store has a 9% chance of being out of an item on two days in a row. What is the probability that the item will be in stock both days?
  • A) 72%
  • B) 74.61%
  • C) 75%
  • D) 78%
  • E) 92%
  1. A water pipe has a 6% chance of leaking each day. What is the chance it won't leak for two consecutive days?
  • A) 84.2%
  • B) 87%
  • C) 88.36%
  • D) 89%
  • E) 94%
  1. If there is a 12% chance of a server failing, what is the chance that two servers will not fail?
  • A) 62.5%
  • B) 67%
  • C) 72%
  • D) 77.44%
  • E) 88%
  1. A lamp has a 1% chance of being defective. What is the probability that out of two lamps, neither is defective?
  • A) 88.11%
  • B) 92.5%
  • C) 95.55%
  • D) 98.01%
  • E) 99%
  1. The chance of a machine breaking down is 18%. What is the chance it won't break down on two consecutive uses?
  • A) 56.25%
  • B) 59.1%
  • C) 65.56%
  • D) 67.24%
  • E) 82.36%

Answers

  1. B) 49%
  2. B) 72.25%
  3. C) 90.25%
  4. A) 25%
  5. E) 77.44%
  6. D) 96.04%
  7. D) 81%
  8. C) 90.25%
  9. C) 75%
  10. D) 64%
  11. B) 60.84%
  12. E) 72%
  13. D) 77.37%
  14. E) 96%
  15. D) 94.09%
  16. B) 74.61%
  17. C) 88.36%
  18. D) 77.44%
  19. D) 98.01%
  20. D) 67.24%
Clap here if you liked the blog