Date | May 2021 | Marks available | 2 | Reference code | 21M.1.SL.TZ1.9 |
Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 1 |
Command term | Find and Hence | Question number | 9 | Adapted from | N/A |
Question
A biased four-sided die, A, is rolled. Let X be the score obtained when die A is rolled. The probability distribution for X is given in the following table.
A second biased four-sided die, B, is rolled. Let Y be the score obtained when die B is rolled.
The probability distribution for Y is given in the following table.
Find the value of p.
Hence, find the value of E(X) .
State the range of possible values of r.
Hence, find the range of possible values of q.
Hence, find the range of possible values for E(Y).
Agnes and Barbara play a game using these dice. Agnes rolls die A once and Barbara rolls die B once. The probability that Agnes’ score is less than Barbara’s score is 12.
Find the value of E(Y).
Markscheme
recognising probabilities sum to 1 (M1)
p+p+p+12p=1
p=27 A1
[2 marks]
valid attempt to find E(X) (M1)
1×p+2×p+3×p+4×12p(=8p)
E(X)=167 A1
[2 marks]
0≤r≤1 A1
[1 mark]
attempt to find a value of q (M1)
0≤1-3q≤1 OR r=0⇒q=13 OR r=1⇒q=0
0≤q≤13 A1
[2 marks]
E(Y)=1×q+2×q+3×q+4×r (=2+2r OR 4-6q) (A1)
one correct boundary value A1
1×13+2×13+3×13+4×0 OR
OR
OR
OR
OR
A1
[3 marks]
METHOD 1
evidence of choosing at least four correct outcomes from
(M1)
OR OR (A1)
solving for either or M1
OR OR
OR
EITHER two correct values
and A1A1
OR one correct value
OR A1
substituting their value for or A1
OR
THEN
A1
METHOD 2 (solving for )
evidence of choosing at least four correct outcomes from
(M1)
OR OR (A1)
rearranging to make the subject M1
M1
A1
A1
[6 marks]