Question
If ๐ is a binomial random variable with ๐=16 trials and ๐=0.35 probability of success on a given trial, find the probability that we will see 1, 2, or 3 successes.
261
likes1304 views
Answer to a math question If ๐ is a binomial random variable with ๐=16 trials and ๐=0.35 probability of success on a given trial, find the probability that we will see 1, 2, or 3 successes.
Miles
4.9114 Answers
Given:
n = 16
p = 0.35
P(X = k) = \binom{16}{k} (0.35)^k (0.65)^{16-k}
Calculate \( P(X = 1) \):
\binom{16}{1}(0.35)^1(0.65)^{15}=16\cdot0.35\cdot(0.65)^{15}\approx0.0087
Calculate \( P(X = 2) \):
\binom{16}{2}(0.35)^2(0.65)^{14}=\frac{16 \cdot15}{2}\cdot(0.35)^2\cdot(0.65)^{14}\approx0.0353
Calculate \( P(X = 3) \):
\binom{16}{3}(0.35)^3(0.65)^{13}=\frac{16 \cdot15 \cdot14}{6}\cdot(0.35)^3\cdot(0.65)^{13}\approx0.0190
Sum the probabilities:
P(X=1)+P(X=2)+P(X=3)=0.063
Therefore, the probability of seeing 1, 2, or 3 successes is:
\boxed{0.063}
Calculate \( P(X = 1) \):
Calculate \( P(X = 2) \):
Calculate \( P(X = 3) \):
Sum the probabilities:
Therefore, the probability of seeing 1, 2, or 3 successes is:
Frequently asked questions (FAQs)
Convert 5ฯ/6 radians to degrees.
+
What is the value of hyperbolic sine (sinh) for x equal to 2.5?
+
Question: Find the derivative of f(x) = 5x^3 - 2e^x + โx - ln(x).
+
New questions in Mathematics