SPM.2.SL.TZ0.4

pestleMathematicsAASLPaper 2SPM· sl-4-8-binomial-distributionsource ↗

A six-sided biased die is weighted in such a way that the probability of obtaining a “six” is $\frac{7}{{10}}$ .

The die is tossed five times. Find the probability of obtaining at most three “sixes”.

[3]

The die is tossed five times. Find the probability of obtaining the third “six” on the fifth toss.

[3]

Markscheme / solution

recognition of binomial (M1)

X ~ B(5, 0.7)

attempt to find P (X ≤ 3) M1

= 0.472 (= 0.47178) A1

[3 marks]

recognition of 2 sixes in 4 tosses (M1)

P (3rd six on the 5th toss) $= \left[ {\left( {\begin{array}{*{20}{c}} 4 \\ 2 \end{array}} \right) \times {{\left( {0.7} \right)}^2} \times {{\left( {0.3} \right)}^2}} \right] \times 0.7 \left( {=0.2646 \times 0.7} \right)$ A1

= 0.185 (= 0.18522) A1

[3 marks]

Examiners’ report

[N/A]