1. The events "First digit less than 3" and "Second digit greater than 7" are independent events. The probability of the first digit being less than 3 is 2/10 = 0.2, and the probability of the second digit being greater than 7 is also 2/10 = 0.2. Since the events are independent, the probability of both events occurring is the product of their individual probabilities: 0.2 * 0.2 = 0.04
2. The events "First digit is prime" and "Second digit is prime" are not independent events, as the prime numbers for the first and second digits are limited. The prime numbers less than three are 2, and the prime numbers greater than 7 are 7. Therefore, the probability of the first digit being prime is 1/10 = 0.1, and the probability of the second digit being prime is also 1/10 = 0.1. Since the events are not independent, we cannot simply multiply their probabilities. Thus, the probability of both events occurring is 0.1 (the only prime number in the first position) * 0.1 (the only prime number in the second position) = 0.01.
Regarding Independent events and coditional probability, answer the question for the following events:
1. First digital less than 3, second digital greater than 7.
2. First digit is prime, second digital is prime.
For each set of event above, find the probability of both occurring.
3 answers
In question , how is the second one (7) is equal to 2
I apologize for the confusion in my previous response. The prime numbers less than three are 2, and the prime numbers less than or equal to 7 are 2, 3, 5, and 7. Therefore, the probability of the first digit being prime is 4/10 = 0.4.
The probability of the second digit being prime is also 4/10 = 0.4. Since the events are not independent, we cannot simply multiply their probabilities. So, the probability of both events occurring is 0.4 (the probability of a prime number for the first digit) * 0.4 (the probability of a prime number for the second digit) = 0.16.
Thank you for pointing out the error, and I apologize for any confusion caused.
The probability of the second digit being prime is also 4/10 = 0.4. Since the events are not independent, we cannot simply multiply their probabilities. So, the probability of both events occurring is 0.4 (the probability of a prime number for the first digit) * 0.4 (the probability of a prime number for the second digit) = 0.16.
Thank you for pointing out the error, and I apologize for any confusion caused.