Probability
Tested in 8 real MPSC questions across 4 years (2015–2021). See it in context on the interactive Concept Graph →
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Real questions that test this
6 पुरुष व 5 महिला यांच्या गटातून 5 सदस्यीय समिती स्थापन करावयाची आहे. यातून 3 पुरुष व 2 महिला असतील अशी समिती किती प्रकारे तयार करता येईल ? / A five-member committee is to be formed from the group comprising of 6 men and 5 women. In how many different ways can the committee be formed with 3 men and 2 women ?
To form a committee of 3 men and 2 women from 6 men and 5 women, we use combinations. Ways to select 3 men out of 6 is 6C3 = 20. Ways to select 2 women out of 5 is 5C2 = 10. Total ways = 6C3 * 5C2 = 20 * 10 = 200.
दिनूचे घर ते शाळा या दरम्यान 23 बस उपलब्ध आहेत. जर घरापासून शाळेपर्यंत वेगवेगळ्या बसने जाऊन परतायचे असेल तर दिनूला किती पद्धतींनी ये-जा करणे शक्य आहे ? There are 23 buses available between Dinu’s house and his school. How many ways are possible for Dinu to go from his house to school and return using different buses ?
Dinu has 23 buses to go from house to school. To return using a *different* bus, he has 22 options available. Total ways = 23 * 22 = 506.
15 पुरुष व 7 महिला यांच्यामधून 10 सदस्यीय समिती गठीत करावयाची आहे. समितीत कमीतकमी 6 महिलांचा समावेश असेल अशी समिती किती प्रकारे तयार करता येईल ?
Total committee size = 10 members from 15 men and 7 women, with AT LEAST 6 women. Cases: 1) 6 women and 4 men: 7C6 * 15C4 = 7 * 1365 = 9555. 2) 7 women and 3 men: 7C7 * 15C3 = 1 * 455 = 455. Total ways = 9555 + 455 = 10010.
एका पिशवीमध्ये 2 लाल, 3 हिरवे आणि 2 निळे चेंडू आहेत. जर यादृच्छिकतेने दोन चेंडू काढले तर त्यात एकही चेंडू निळा नसण्याची संभाव्यता किती?
Total balls = 7 (2 red, 3 green, 2 blue). Non-blue balls = 5 (2 red + 3 green). Probability of drawing 2 non-blue balls is C(5,2) / C(7,2).