Tickst number 1-15are placed in a hat ,2 Tickets Are drawn at random without replacement find the probability that both Numbers Are Greater then 9
B.) the First Number is Prime and the Second number is Composite?
a) number greater than 9: 10,11,12,13,14,15
so 6 of them
prob(as stated) = 9/15 = 3/5
b) do it the same way, count how many are prime, and how many are composite
To find the probability in both cases, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
A) Probability that both numbers are greater than 9:
Total number of tickets = 15 (as there are 15 tickets in the hat)
To determine the number of favorable outcomes, we need to count the number of tickets greater than 9.
Number of tickets greater than 9 = 15 - 9 = 6
As we are drawing 2 tickets without replacement, the number of favorable outcomes for the first draw is 6, and for the second draw, it will be 5 (as there will be one less ticket in the hat).
To calculate the probability, we need to calculate the probability of both events happening.
Probability = (Number of favorable outcomes for the first draw / Total number of tickets) * (Number of favorable outcomes for the second draw / Total number of tickets after the first draw).
Probability = (6 / 15) * (5 / 14) = 0.2 * 0.357 ≈ 0.0714
Therefore, the probability that both numbers drawn are greater than 9 is approximately 0.0714 (or 7.14%).
B) Probability that the first number is prime and the second number is composite:
Total number of tickets = 15 (as there are 15 tickets in the hat)
To determine the number of favorable outcomes, we need to count the number of prime numbers and composite numbers.
Number of prime numbers = 4 (11, 13, 2, 3)
Number of composite numbers = 15 - 4 = 11
Since we are drawing 2 tickets without replacement, the number of favorable outcomes for the first draw is 4 (prime numbers), and for the second draw, it will be 11 (composite numbers).
To calculate the probability, we use the same formula as before:
Probability = (Number of favorable outcomes for the first draw / Total number of tickets) * (Number of favorable outcomes for the second draw / Total number of tickets after the first draw).
Probability = (4 / 15) * (11 / 14) ≈ 0.1778 * 0.7857 ≈ 0.1395
Therefore, the probability that the first number drawn is prime and the second number drawn is composite is approximately 0.1395 (or 13.95%).