Just to reblog this earlier post on a really challenging Probability O Level Question.
Also, do check out my other related posts on Probability:
Probability is becoming a really important branch of mathematics. One of the most famous Singaporean mathematicians is Professor Louis Chen Hsiao Yun who has a theorem named after him! (Stein-Chen method of Poisson approximation) Professor Chen researches on Probability.
To begin your journey in Probabilty, Introduction to Probability, 2nd Edition
is a good book to start learning from. An intuitive, yet precise introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. You may also wish to refer to our comprehensive list of Recommended Undergraduate Books.
(One of the best books to begin your journey in studying the mysterious topic of Probability)
A bag A contains 9 black balls, 6 white balls and 3 red balls. A bag B contains 6 black balls, 2 white balls and 4 green balls. Ali takes out 1 ball from each bag randomly. When Ali takes out 1 ball from one bag, he will put it into the other bag and then takes out one ball from that bag. Find the probability that
(a) the ball is black from bag A, followed by white from bag B,
(b) both the balls are white in colour,
(c) the ball is black or white from bag B, followed by red from bag A,
(d) both the balls are of different colours,
(e) both the balls are not black or white in colours.
Solution:
(a) $latex displaystylefrac{9}{18}timesfrac{2}{13}=frac{1}{13}$
(b) Probability of white ball from bag A, followed by white ball from bag B=$latex displaystyle=frac{1}{2}timesfrac{6}{18}timesfrac{3}{13}=frac{1}{26}$
Probability of white from B, followed…
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Singapore Maths Tuition 
Hi
Xinmin Secondary 2010 Prelim Paper I Q24 Solution (Challenging/Difficult Probability O Level Question):
For xinmin probability question . Why is 1/2 not needed for parts a and c ? Whereas it’s needed for the other parts of the question ?
Thanks.
Regards
Agnes
Sent from Yahoo Mail on Android
From:”Singapore Maths Tuition” Date:Sun, 22 Mar, 2015 at 14:59 Subject:[New post] Xinmin Secondary 2010 Prelim Paper I Q24 Solution (Challenging/Difficult Probability O Level Question)
mathtuition88 posted: “Just to reblog this earlier post on a really challenging Probability Question.”
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For parts a and c, the order of taking the balls from the bags is specified. For instance, in part a, we know that a black ball is taken from Bag A first, then from Bag B.
In the other parts of the question, the order is not specified, hence there is a 50% chance that one starts picking from Bag A, and a 50% chance that one starts picking from Bag B, hence the 1/2.
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