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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
Options
0.0875
1/16
0.1125
none of these
Solution
\[0 . 0875\]
\[\text{ Here, there are total 5 ways by which India can get at least 7 points } .\]
\[\left( 1 \right) 2 \text{ points } + 2 \text{ points } + 2 \text{ points} + 2 \text{ points } = \left( 0 . 5 \times 0 . 5 \times 0 . 5 \times 0 . 5 \right)\]\[\left( 2 \right) 1 \text{ point }+ 2 \text{ points } + 2 \text{ points } + 2 \text{ points } = \left( 0 . 05 \times 0 . 5 \times 0 . 5 \times 0 . 5 \right)\]
\[\left( 3 \right) 2 \text{ points }+ 1 \text{ point} + 2 \text{ points } + 2 \text{ points } = \left( 0 . 5 \times 0 . 05 \times 0 . 5 \times 0 . 5 \right)\]
\[\left( 4 \right) 2 \text{ points}+ 2 \text{ points} + 1 \text{ point }+ 2 \text{ points} = \left( 0 . 5 \times 0 . 5 \times 0 . 05 \times 0 . 5 \right)\]
\[\left( 5 \right) 2 \text{ points }
+ 2 \text{ points } + 2 \text{ points } + 1 \text{ point } = \left( 0 . 5 \times 0 . 5 \times 0 . 5 \times 0 . 05 \right)\]
\[P\left( \text{ atleast 7 points }\right) = 0 . 5 \times 0 . 5 \times 0 . 5 \times 0 . 5 + 4\left[ 0 . 05 \times 0 . 5 \times 0 . 5 \times 0 . 5 \right]\]
\[ = 0 . 0625 + 4\left( 0 . 00625 \right)\]
\[ = 0 . 0625 + 0 . 025\]
\[ = 0 . 0875\]
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