Probability 5 Question 10
10. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0,1 and 2 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
$(1992,2 M)$
(a) 0.8750
(b) 0.0875
(c) 0.0625
(d) 0.0250
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Answer:
Correct Answer: 10. (b)
Solution:
- India play 4 matches and getting at least 7 points. It can only be possible in $W W W D$ or $W W W W$ position, where $W$ represents two points and $D$ represents one point.
Therefore, the probability of the required event
$$ \begin{aligned} & ={ }^{4} C _3(0.05)(0.5)^{3}+{ }^{4} C _4(0.5)^{4} \\ & =4(0.05)+0.5^{3}=0.0875 \end{aligned} $$
