Question

India play two matches each with West Indies and Australia. In any match the probabilities of India getting 0,1 and 2 points are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is
(a) 0.0875
(b) 1/16
(c) 0.1125
(d) none of these

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)0.0875 \\ \text{Here, there are total 5 ways by which India can get at least 7 points.} \\ \left(1\right)2\text{points+}2\mathrm{points}+2\mathrm{points}+2\mathrm{points}=\left(0.5\times 0.5\times 0.5\times 0.5\right) \\ \left(2\right)1\text{point+}2\mathrm{points}+2\mathrm{points}+2\mathrm{points}=\left(0.05\times 0.5\times 0.5\times 0.5\right) \\ \left(3\right)2\text{points+}1\mathrm{point}+2\mathrm{points}+2\mathrm{points}=\left(0.5\times 0.05\times 0.5\times 0.5\right) \\ \left(4\right)2\text{points+}2\mathrm{points}+1\mathrm{point}+2\mathrm{points}=\left(0.5\times 0.5\times 0.05\times 0.5\right) \\ \left(5\right)2\text{points+}2\mathrm{points}+2\mathrm{points}+1\mathrm{point}=\left(0.5\times 0.5\times 0.5\times 0.05\right) \\ \mathrm{P}\left(\mathrm{atleast}7\mathrm{points}\right)=0.5\times 0.5\times 0.5\times 0.5+4\left[0.05\times 0.5\times 0.5\times 0.5\right] \\ =0.0625+4\left(0.00625\right) \\ =0.0625+0.025 \\ =0.0875 \end{gathered}$$