First slide

Theorems of probability

Question

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

Moderate

A

0.8750
B

0.0625
C

0.0875
D

0.0250

Solution

P(at least 7 points) = P(7 points) + P(8 points)
['.' at most 8 points can be scored]
Now, 7 points can be scored by scoring 2 points in 3 matches and 1 point in one match. Similarly, 8 points can be scored by
scoring 2 points in each of 4 matches. Therefore, the required probability is
$\begin{array}{l} ^{4} C_{1} \times [P (2 points)]^{3} P (1 point) + [P (2 points)]^{4} \\ = 4 (0.5)^{3} \times 0.05 + (0.50)^{4} \\ = 0.0250 + 0.0625 = 0.0875 \end{array}$

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