Two out of every 10 students in a school have a dog. Expressed as a decimal to the nearest hundredth, what is the probability that exactly 2 out of 6 students in a given class have a dog? (1 point)
0.33
0.02
0.20
0.25
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
.2^2 * .8^4 = ?
0.25
To find the probability, we need to calculate the probability of exactly 2 out of 6 students having a dog.
The given statement tells us that 2 out of every 10 students in the school have a dog. We can express this as a fraction: 2/10.
Now, let's calculate the probability for the given class. We have 6 students in the class and we want to find the probability that exactly 2 of them have a dog.
To calculate this probability, we need to use the binomial probability formula:
P(x=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- P(x=k) is the probability of getting exactly k successes (2 students having a dog)
- n is the total number of trials (6 students in the class)
- k is the number of successes we want (2 students having a dog)
- p is the probability of success (2/10 or 0.2)
- (n choose k) is the binomial coefficient, calculated as n! / (k! * (n-k)!)
Let's calculate it step by step:
1. Calculate the binomial coefficient: (6 choose 2) = 6! / (2! * (6-2)!). This results in 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15.
2. Calculate p^k: (0.2)^2 = 0.04.
3. Calculate (1-p)^(n-k): (1-0.2)^(6-2) = 0.8^4 = 0.4096.
4. Multiply the results: P(x=k) = 15 * 0.04 * 0.4096 = 0.024576.
So, the probability that exactly 2 out of 6 students in the given class have a dog is 0.024576, which when rounded to the nearest hundredth is 0.02.
Therefore, the correct answer is 0.02.