[amp_mcq option1=”20%” option2=”25%” option3=”30%” option4=”40%” correct=”option3″]<\/p>\n
The correct answer is $\\boxed{\\text{C. 30%}}$.<\/p>\n
The probability of event A happening, given that event B has already happened, is called the conditional probability of A given B, and is denoted by $P(A|B)$. It can be calculated using the following formula:<\/p>\n
$$P(A|B) = \\frac{P(A \\cap B)}{P(B)}$$<\/p>\n
In this case, event A is picking a red ball, and event B is mixing the contents of Bags A and B. The probability of picking a red ball from Bag A is $0.2$, and the probability of picking a red ball from Bag B is $0.3$. The probability of mixing the contents of Bags A and B is $1$, since it is certain that the contents will be mixed. Therefore, the conditional probability of picking a red ball given that the contents of Bags A and B have been mixed is:<\/p>\n
$$P(A|B) = \\frac{P(A \\cap B)}{P(B)} = \\frac{0.2 + 0.3}{1} = 0.3$$<\/p>\n
Therefore, the probability of picking a red ball is $\\boxed{\\text{30%}}$.<\/p>\n
Option A is incorrect because it is the probability of picking a red ball from Bag A, not from the mixture of Bags A and B. Option B is incorrect because it is the average of the probabilities of picking a red ball from Bags A and B, but these probabilities are not equally likely. Option D is incorrect because it is the probability of picking a red ball from Bag B, not from the mixture of Bags A and B.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”20%” option2=”25%” option3=”30%” option4=”40%” correct=”option3″]<\/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-20295","post","type-post","status-publish","format-standard","hentry","category-probability-and-statistics","no-featured-image-padding"],"yoast_head":"\n