Probability Topical Question [Pearson Edexcel Mathematics B (4MB1) 2014-2016]

 

1	(Edexcel/Math B/2014/jan/paper01/q15) A box contains balls of different colours. The box is opened and a ball is selected at random. The probability that the ball is white is 0.9 and the probability that the ball is black is 0.04 (a) Write down the probability that the ball is either white or black. ....... (1) (b) Find the probability that the ball is neither white nor black....... (2) (Total for Question 15 is 3 marks)
2	(Edexcel/Math B/2014/jan/paper02/q6) On school days, Fatima goes to school by bus. The probability that it will rain on a school day is $\frac 27$ When it rains, the probability that the bus will be late is $\frac15$ When it does not rain, the probability that the bus will not be late is $\frac56$ (a) Complete the probability tree diagram......(3) Calculate the probability that on a school day, (b) it will be raining and the bus will be late, (2) (c) the bus will be late. (3) . (Total for Question 6 is 8 marks)
3	(Edexcel/Math B/2014/janR/paper02/q9) Three bags of counters are used in a game. At the start of the game Bag A contains 5 red counters and 4 white counters. Bag B contains 4 red counters and 1 white counter. Bag C contains 3 red counters and 3 white counters. The game begins by taking at random a counter from Bag A. If the counter is red, a counter is then taken at random from Bag B. If the counter taken from Bag A is white, a counter is taken at random from Bag C. (a) Complete the probability tree diagram. (3) (b) Show that the probability that the second counter taken is red is twice the probability that the second counter taken is white. (5) Given that the second counter taken is red, (c) find the probability that the first counter taken is white. (3) (Total for Question 9 is 11 marks)
4	(Edexcel/Math B/2014/june/paper01/q27) An archer shoots an arrow at a target. The probability that he will hit the target is $\frac 34$ After the first shot, the target is moved further away from the archer. The archer shoots a second arrow at the target and the probability that he will hit the target is now $\frac 35$ (a) Complete the probability tree diagram. (2) Calculate the probability that the archer will (b) hit the target with his first shot but miss the target with his second shot, (2) (c) hit the target at least once if he takes both shots.(3) (Total for Question 27 is 7 marks)
5	(Edexcel/Math B/2014/june/paper02/q6) There are 159 people living in a street. The table below shows information about the number of people living in each of 30 houses in the street. Number (n) of people living in a house Number of houses with (n) people living in the house 1 2 2 3 3 1 4 4 5 3 6 6 7 8 8 2 9 1 (a) Find (i) the modal number of people living in a house, (ii) the median number of people living in a house, (iii) the mean number of people living in a house. (5) Two houses in the street are chosen at random. (b) Calculate the probability that 4 people live in one of the houses and 2 people live in the other of the houses. (2) One of the people living in the street is chosen at random. (c) Find the probability that this person lives in a house in which at least 5 people live. (2)  (Total for Question 6 is 9 marks)
	to be continued.....

Probability (2014-2016)

1.   (a) $0.94 $ (b) $0.06 $  
2.   (a) $\frac{5}{7}, \frac{4}{3}, \frac{1}{5}, \frac{5}{6}, \frac{1}{6} $ (b) $ \frac{2}{35} \quad $ (c) $ \frac{37}{210} $
3.   (a) $\frac{4}{9}, \frac{4}{5}, \frac{1}{5}, \frac{3}{6}, \frac{3}{6}$ (b) show (c) $\frac{1}{3}$.
4.   (a) $ \frac{1}{4} ; \frac{3}{5}, \frac{2}{5} ; \frac{3}{5}, \frac{2}{5}$ (b) $ \frac{6}{20}$ (c) $ \frac{18}{20} $ 
5.   (a)(i) 7 (ii) 6  (iii) 5.3  (b) $\frac{24}{870} \quad$ (c) $\frac{132}{159}$
6.   (a) $\frac{3}{10} , \frac{6}{9}, \frac{3}{9} , \frac{7}{9}, \frac{2}{9}$ (b) $\frac{42}{90}$ 
7.   (a) $\frac{20}{50}, \frac{29}{49}, \frac{20}{49}, \frac{30}{49}, \frac{19}{49}$ (b) $\frac{870}{2450}$ (c) $\frac{2100}{2970}$
8.   (a) $\frac{4}{9}$ (b) $\frac{1}{6}$ (c) $\frac{5}{18} \quad $
9.   (a) 120,96,48,24 (b) $\frac {120}{360}$ (c) $\frac {2}{5}$ (d) $0.204$
10.   (a) $0.24$ (b) $144 \quad$ 
11.   (a) $\frac{7}{20}$ (b) $\frac{132}{380}$
12.   (a) $\frac{4}{11} ; \frac{6}{10}, \frac{4}{10} ; \frac{7}{10}, \frac{3}{10} \quad$ (b) (i) $\frac{28}{110}$ (ii) $\frac{68}{110}$ (c) show 
13.   (a) $x=\frac{1}{7} / 0.143$ (b) $\frac{13}{49}, 0.265,0.266$.
14.   (a) $\frac{8}{14}, \frac{6}{14}, \frac{9}{14}, \frac{5}{14}, \frac{7}{13}, \frac{6}{13}, \frac{5}{13}, \frac{8}{13}, \frac{5}{13}, \frac{4}{13}$ (b)(i) $\frac{12}{65}$ (ii) $\frac{53}{65}$ (iii) $\frac{60}{91}$
15.   (a) 36 (b) y=44 
16.   (a) $\frac{4}{5}, \frac{1}{5}, p, 1-p, q, 1-q \quad$ (b)(i) $\frac{1}{5} \times(1-q)=\frac{3}{20} \quad$ (ii) $q=\frac{1}{4}$ (c)(i) $\frac{4}{5}(1-p)+\frac{1}{5} \times \frac{1}{4}=\frac{7}{12}$ (ii) $p=\frac{1}{3}$ (d) $\frac{29}{150}$
17.   (a) $\frac{1}{3}, \frac{2}{3}, p, 1-p, \frac{4}{5}, \frac{1}{5}$ (b) $\frac 13 p+ \frac 23 \times \frac 45$ (c) $p=\frac{1}{4} \quad $ 
18.   $\frac 19$
19.   (a) $ 0.25,0.7,0.3,0.6,0.4 $ (b)(i) $ 0.1$  (ii) $ 0.325 $ (c) $ 0.31$