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

(1992,2M)

(a) 0.8750

(b) 0.0875

(c) 0.0625

(d) 0.0250

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Answer:

Correct Answer: 10. (b)

Solution:

  1. India play 4 matches and getting at least 7 points. It can only be possible in WWWD or WWWW position, where W represents two points and D represents one point.

Therefore, the probability of the required event

$$ \begin{aligned} & ={ }^{4} C _3(0.05)(0.5)^{3}+{ }^{4} C _4(0.5)^{4} \ & =4(0.05)+0.5^{3}=0.0875 \end{aligned} $$



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