The probability that a student uses Smarthinking online tutoring on a regular basis is 0.41. In a group of 21 students, what is the probability that exactly 5 of them use Smarthinking Online Tutoring on a regular basis?
Write only a number as your answer. Round to 4 decimal places (for example 0.2416). Do not write as a percentage.
pr(5)=.41^5*.59^(21-5)
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To find the probability that exactly 5 out of 21 students use Smarthinking Online Tutoring on a regular basis, we can use the binomial probability formula.
The binomial probability formula is:
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))
where:
P(x) represents the probability of getting exactly x successes,
n represents the total number of trials or students in this case,
x represents the number of successes we are interested in (i.e., 5),
p represents the probability of success in a single trial (i.e., 0.41), and
(1-p) represents the probability of failure in a single trial (i.e., 1 - 0.41 = 0.59).
Now we can plug in the values into the formula:
P(5) = (21C5) * (0.41^5) * (0.59^(21-5))
To calculate (21C5), the combination value of 21 choose 5, we can use the formula:
(21C5) = 21! / (5! * (21-5)!)
Simplifying the calculations:
(21C5) = (21 * 20 * 19 * 18 * 17) / (5 * 4 * 3 * 2 * 1)
Now we can substitute the values into the main formula:
P(5) = (21C5) * (0.41^5) * (0.59^(21-5))
After evaluating the equation, the probability is approximately 0.1742.
Therefore, the probability that exactly 5 out of 21 students use Smarthinking Online Tutoring on a regular basis is 0.1742 (rounded to four decimal places).
To find the probability that exactly 5 out of 21 students use Smarthinking Online Tutoring on a regular basis, we can use the binomial probability formula.
The binomial probability formula is: P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of exactly k successes
n is the total number of trials
k is the number of successes
p is the probability of success for each trial
(1-p) is the probability of failure for each trial
In this case, n = 21, k = 5, and p = 0.41.
Plugging in these values into the formula:
P(X=5) = (21 choose 5) * (0.41)^5 * (1-0.41)^(21-5)
Calculating this using a binomial calculator or software, the probability is approximately 0.1172.
Therefore, the probability that exactly 5 out of 21 students use Smarthinking Online Tutoring on a regular basis is 0.1172.