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  • 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

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

Option: 1

0.0875


Option: 2

\frac{1}{16}


Option: 3

0.1125


Option: 4

None of these


Answers (1)

best_answer

\mathrm{P\left(E_0\right)=0.45, \quad P\left(E_1\right)=0.05, \quad P\left(E_2\right)=0.50}

For 7 points there should be at least three instances of 2 points and one of 1 or 2 points.

\therefore   the required probability

\begin{aligned} & \mathrm{=P\left(E_2 E_2 E_2 E_2\right)+P\left(E_2 E_2 E_2 E_1\right)+P\left(E_2 E_2 E_1 E_2\right)+P\left(E_2 E_1 E_2 E_2\right)+P\left(E_1 E_2 E_2 E_2\right)} \\ \\& = \mathrm{\left\{P\left(E_2\right)\right\}^4+4\left\{P\left(E_2\right)\right\}^3 \cdot P\left(E_1\right)} \\ \\& =(0.50)^4+4(0.50)^3 \cdot(0.05)=0.0875 . \end{aligned}

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shivangi.bhatnagar

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