(a) A fair, six-sided dice is thrown twice. What is the probability that a 3 is thrown on both occasions? [2]
(b) A company has offices in Llanelli, Caernarfon, Newtown and Ebbw Vale. Its national committee is made up of workers from these four offices.
The pie chart below shows what fraction of the committee members come from each office.
There is an equal number of members from Newtown and Ebbw Vale. A member is chosen at random from this committee to be its chairperson.
(i) The probability that the chosen member works at the Llanelli office is shown in the table below. Complete the table. [2]
Office
Llanelli
Caernarfon
Newtown
Ebbw Vale
Probability
\(\dfrac{1}{2}\)
(ii) What is the probability that the member chosen as chairperson works at either the Llanelli or the Ebbw Vale office? You must show all your working. [2]
Mark scheme (a)
Scheme
Marks
Comments
1/6 × 1/6
M1
= 1/36
A1
Mark scheme (b)
Scheme
Marks
Comments
4(b)(i) P(Caernarfon) = ¼ or equivalent
B1
Penalise incorrect notation −1 once only in 4(b) CAO.
P(Newtown) AND P(Ebbw Vale) = 1/8 or equivalent
B1
CAO. Do not allow 0·5/4 for 1/8.
4(b)(ii) ½ + 1/8
M1
FT ½ + ‘their P(Eb.V.)’. Provided P(Eb.V)<1 for M1.
= 5/8 or equivalent.
A1
FT answer must be < 1 for A1. Mark final answer Allow 2·5/4 for 5/8 if answer to 4(b)(i) is 0·5/4.
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