Question - Calculating Probability of Independent Events
Solution:
To solve this problem, we need to calculate the probability of two independent events occurring in sequence:1. Picking a prime number card.2. Picking a number greater than 4 card.The sample space consists of 8 cards, numbered from 1 to 8. Among these cards, the prime numbers are 2, 3, 5, and 7.Probability of picking a prime number card = number of prime cards / total number of cardsP(prime) = 4/8 = 1/2After picking a prime number, you replace the card and pick again. The number of cards greater than 4 are 5, 6, 7, and 8.Probability of picking a number greater than 4 = number of cards greater than 4 / total number of cardsP(greater than 4) = 4/8 = 1/2Since these are independent events, we can multiply the probabilities:P(prime and greater than 4) = P(prime) * P(greater than 4)P(prime and greater than 4) = (1/2) * (1/2)P(prime and greater than 4) = 1/4Converting this into a percentage, we get:P(prime and greater than 4) = (1/4) * 100% = 25%Rounded to the nearest tenth of a percent, the answer remains 25.0%.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com