[amp_mcq option1=”$$\\frac{1}{4}$$” option2=”$$\\frac{4}{{25}}$$” option3=”$$\\frac{1}{3}$$” option4=”$$\\frac{{29}}{{50}}$$” correct=”option3″]<\/p>\n
The correct answer is $\\boxed{\\frac{1}{3}}$.<\/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, we are given that $P(X) = \\frac{1}{4}$, $P(Y) = \\frac{1}{3}$, and $P(X \\cap Y) = \\frac{1}{12}$. We can use these values to calculate $P(Y|X)$ as follows:<\/p>\n
$$P(Y|X) = \\frac{P(X \\cap Y)}{P(X)} = \\frac{\\frac{1}{12}}{\\frac{1}{4}} = \\frac{1}{3}$$<\/p>\n
Therefore, the probability of event Y happening, given that event X has already happened, is $\\frac{1}{3}$.<\/p>\n
Option A is incorrect because it is the probability of event X happening, not the probability of event Y happening given that event X has already happened.<\/p>\n
Option B is incorrect because it is the probability of event Y happening, but it is not calculated using the correct formula.<\/p>\n
Option C is incorrect because it is the probability of event X happening, but it is not the probability of event Y happening given that event X has already happened.<\/p>\n
Option D is incorrect because it is the probability of event Y happening, but it is not calculated using the correct formula.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”$$\\frac{1}{4}$$” option2=”$$\\frac{4}{{25}}$$” option3=”$$\\frac{1}{3}$$” option4=”$$\\frac{{29}}{{50}}$$” 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-20305","post","type-post","status-publish","format-standard","hentry","category-probability-and-statistics","no-featured-image-padding"],"yoast_head":"\n