Question

devonports daffodil festival holds an egg hunt every year. the organizers hide plastic eggs filled with small toys and candy throughout the town center. theres a 5% chance that an egg also has a golden ticket inside that can be redeemed for a larger prize. cody finds 12 eggs during the egg hunt. how likely is it that at least 1 of his eggs has a golden ticket inside? which simulation could be used to fairly represent the situation? use a computer to randomly generate 12 numbers from 1 to 20. each time 1 appears, it represents a golden ticket. 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, 5 times. each time 1 appears, it represents a golden ticket. create a spinner with 5 equal sections. color 1 section gold and the remaining sections white. spin the spinner 12 times. each time the spinner lands on the gold section, it represents a golden ticket.

Explanation:

Step1: Calculate the probability of no golden ticket

The probability that an egg does not have a golden ticket is \(1 - 0.05=0.95\). For \(n = 12\) eggs, the probability that none of the 12 eggs has a golden ticket is \(P(X = 0)=(0.95)^{12}\).

Step2: Calculate the probability of at least one golden ticket

The probability of at least one golden ticket is \(P(X\geq1)=1 - P(X = 0)\).

Now for the simulation:

• The probability of getting a golden ticket is \(5\%=\frac{1}{20}\).
• We need to simulate 12 trials (since Cody found 12 eggs).
• In the first option: Using a computer to generate 12 numbers from 1 - 20. The probability of getting a 1 (representing a golden ticket) in each trial is \(\frac{1}{20}=0.05\), and we have 12 trials.
• In the second option: We only pick 5 times, but we need 12 - trial simulation.
• In the third option: The probability of landing on the gold - section is \(\frac{1}{5}=0.2

eq0.05\)

Answer:

The first simulation (Use a computer to randomly generate 12 numbers from 1 to 20. Each time 1 appears, it represents a golden ticket) is the correct one.