Question

read the story. quartz crusade is abduls favorite video game. each level in the game is a new cave full of hidden gems. 70% of the time, abdul completes a level on his first try. he wants to complete 3 levels today. how likely is it that abdul will complete all of them on his first try? which simulation could be used to fairly represent the situation? flip a pair of coins 3 times. each time at least one coin lands on tails, it represents abdul completing a level on his first try. create a deck of 20 cards, each labeled with a different number from 1 to 20. pick a card, then return it to the deck, 10 times. each time a number greater than 6 appears, it represents abdul completing a level on his first try. use a computer to randomly generate 3 numbers from 1 to 10. each time a number greater than 3 appears, it represents abdul completing a level on his first try.

Explanation:

Step1: Analyze probability of original event

The probability that Abdul completes a level on his first try is 70% or 0.7.

Step2: Analyze coin - flip simulation

When flipping a pair of coins, the probability that at least one coin lands on tails: \(P(\text{at least one tails})=1 - P(\text{both heads})=1-\frac{1}{2}\times\frac{1}{2}=\frac{3}{4} = 0.75
eq0.7\).

Step3: Analyze card - pick simulation

In a deck of 20 cards numbered 1 - 20, the probability of picking a number greater than 6 is \(\frac{20 - 6}{20}=\frac{14}{20}=0.7\), but the process of picking 10 times is not relevant as we only need to simulate 3 levels.

Step4: Analyze number - generation simulation

When generating a number from 1 - 10, the probability of getting a number greater than 3 is \(\frac{10 - 3}{10}=0.7\), and generating 3 numbers simulates the 3 levels. So this simulation is appropriate.

Answer:

Use a computer to randomly generate 3 numbers from 1 to 10. Each time a number greater than 3 appears, it represents Abdul completing a level on his first try.