Question

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n equals 9​, p equals 0.8​, x less than or equals 3

Answer 1

Answer: 0.0031

Step-by-step explanation:

Binomial distribution formula :-

$P(x)=^nC_xp^x(1-p)^{n-x}$, where P(x) is the probability of x successes in the n independent trials of the experiment and p is the probability of success.

Given : A binomial probability experiment is conducted with the given parameters.

$n=9,\ p=0.8,\ x\leq3$

Now, $P(x\leq3)=P(3)+P(2)+P(1)+P(0)$

$=^9C_3(0.8)^3(1-0.8)^{9-3}+^9C_2(0.8)^2(1-0.8)^{9-2}+^9C_1(0.8)^1(1-0.8)^{9-1}+^9C_0(0.8)^0(1-0.8)^9\\\\=\dfrac{9!}{3!6!}(0.8)^3(0.2)^6+\dfrac{9!}{2!7!}(0.8)^2(0.2)^7+\dfrac{9!}{1!8!}(0.8)(0.2)^8+\dfrac{9!}{0!9!}(0.2)^9=0.003066368\approx0.0031$

Hence,  $P(x\leq3)=0.0031$