Solved: A six-sided biased cube is weighted in such a way that the probability of... [IB Mathematics Analysis and Approaches (AA)]

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SLPaper 2

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

The cube is tossed five times. Find the probability of obtaining at most three "sixes".

[3]

Verified

Solution

recognition of binomial (M1)

X ~ B(5, 0.7)

attempt to find P (X ≤ 3) (M1)

=0.472 (= 0.47178)*(A1)

[3 marks]

The cube is tossed five times. Find the probability of obtaining the third "six" on the fifth toss.

[3]

Verified

Solution

recognition of 2 sixes in 4 tosses (M1) P (3rd six on the 5th toss) ${= \left[ {\left( {\begin{matrix} 4 \\ 2 \end{matrix}} \right) \times \left({0.7}\right)^2 \times \left({0.3}\right)^2} \right] \times 0.7 \left( =0.2646 \times 0.7 \right)}$ A1 = 0.185 (= 0.18522) A1 [3 marks]