Conditional Probability
Conditional Probability is a Aptitude concept from the MPSC syllabus, tested in 3 past MPSC questions (2017, 2022, 2025). Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.
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एका वर्गामध्ये 15 मुले आणि 10 मुली आहेत. तीन मुलांची यादृच्छिकपणे (random) निवड करावयाची आहे. एक मुलगी आणि दोन मुले यांची निवड होण्याची शक्यता ___ आहे.
Total persons = 25. Choosing 3 boys out of 15 is C(15,3). Choosing 1 girl and 2 boys is C(10,1) * C(15,2) / C(25,3).
एका पिशवीमध्ये 3 पांढरे, 2 निळे व 5 लाल चेंडू आहेत. जर यादृच्छिक पद्धतीने पिशवीमधून 1 चेंडू जर काढला, तर काढलेला चेंडू लाल नाही, याची संभाव्य्ता किती आहे ?
Total balls = 3 (white) + 2 (blue) + 5 (red) = 10 balls. The probability of getting a red ball is 5/10 = 1/2. Therefore, the probability of not getting a red ball is 1 - 1/2 = 1/2.
एका पिशवीत 4 पांढरे, 3 लाल आणि 6 निळे बॉल आहेत. पिशवीतून यादृच्छिकपणे 3 बॉल काढायचे आहेत. ते सर्व लाल असण्याची शक्यता ________ आहे. A bag contains 4 white, 3 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red is ________.
There are 13 balls, so the number of ways to draw 3 is 13C3 = 286, and there is only 3C3 = 1 way to draw all three red balls; the true probability is 1/286, which is not among the options. MPSC's final answer key gives option (3), 2/91, so that is the answer recorded here.