O-LevelMathematicsStatistics4024/21 · Oct/Nov 2023 · Q811 Marks

A group of 40 children are each asked how many books they read last month. The table shows the results. Number of books | 0 | 1 | 2 | 3 | 4 | 5 Frequency | 7 | 11 | 9 | 5 | 6 | 2 Write down the mode.

(a)(i)A group of 40 children are each asked how many books they read last month. The table shows the results. Number of books | 0 | 1 | 2 | 3 | 4 | 5 Frequency | 7 | 11 | 9 | 5 | 6 | 2 Write down the mode.[1]
(a)(ii)Find the median.[1]
(a)(iii)Calculate the mean.[2]
(a)(iv)One of the 40 children is chosen at random. Find the probability that this child read 4 or more books. Give your answer as a fraction in its simplest form.[2]
(b)(i)There are 10 books on a shelf. 7 of the books are fiction and 3 are non-fiction. Sanjay takes a book from the shelf at random, looks at it and replaces it. He then takes another book from the shelf at random, looks at it and replaces it. Find the probability that one book is fiction and the other book is non-fiction.[2]
(b)(ii)Mona takes 3 books from the 10 books on the shelf at random without replacement. Find the probability that only one of the books she takes is fiction.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[1] (a)(i) 1
[1] (a)(ii) 2
[2] (a)(iii) 1.95
[2] (a)(iii) M1 for ([0x7]+1x11+2x9+3x5+4x6+5x2)/40 oe
[2] (a)(iv) 1/5 cao
[2] (a)(iv) M1 for (6+2)/40 oe
[2] (b)(i) 21/50 oe
[2] (b)(i) M1 for 7/10 x 3/10 [x2] oe
[3] (b)(ii) 7/40 oe
[3] (b)(ii) M2 for 3/10 x 2/9 x 7/8 x 3 oe
[3] (b)(ii) or M1 for 3/10 x 2/9 x 7/8 oe (If 0 scored, SC1 for answer 189/1000 oe)

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