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  4. 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

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Q. 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

IIT JEEIIT JEE 1992Probability

Solution:

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
$ ={}^ 4 C _3 (0.05) ( 0.5)^3 + {}^4 C _4 (0.5)^4 $
$ = [4(0.05) + 0.5 ] (0.5)^3 = 0.0875 $