[amp_mcq option1=”0.0036″ option2=”0.1937″ option3=”0.2234″ option4=”0.3874″ correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\text{B) 0.1937}}$.<\/p>\n
To calculate the probability of exactly 2 defective items in a sample of 10 items, we can use the binomial distribution. The binomial distribution is a probability distribution that describes the number of successes in a sequence of independent experiments each of which yields success with probability $p$. In this case, the experiment is choosing an item from the lot, and the success is choosing a defective item. The probability of success is $p=0.1$, since 10% of the items in the lot are defective. We want to know the probability of getting 2 successes in 10 trials, so $n=10$.<\/p>\n
The probability of exactly 2 defective items is given by the following formula:<\/p>\n
$$P(X=2)=\\binom{n}{2}p^2(1-p)^{n-2}$$<\/p>\n
where $\\binom{n}{2}$ is the binomial coefficient, which is the number of ways to choose 2 items from a set of 10 items. In this case, $\\binom{10}{2}=45$.<\/p>\n
Plugging in $p=0.1$ and $n=10$, we get:<\/p>\n
$$P(X=2)=\\binom{10}{2}(0.1)^2(0.9)^{10-2}=0.1937$$<\/p>\n
Therefore, the probability of exactly 2 defective items in a sample of 10 items is $\\boxed{\\text{B) 0.1937}}$.<\/p>\n
The other options are incorrect because they do not represent the probability of exactly 2 defective items in a sample of 10 items.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”0.0036″ option2=”0.1937″ option3=”0.2234″ option4=”0.3874″ correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[691],"tags":[],"class_list":["post-20324","post","type-post","status-publish","format-standard","hentry","category-probability-and-statistics","no-featured-image-padding"],"yoast_head":"\n