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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, 0.5 and 0.5 respectively. Assuming that the outcomes are independent, the probability of India getting atleast 7 points is
  • a)
    0.0625
  • b)
    0.0250
  • c)
    0.8750
  • d)
    0.0875
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
India plays two matches each with West Indies and Australia. In any ma...
Probability of India getting points in a match

Given, the probabilities of India getting points 0, 1 and 2 in a match are 0.45, 0.5 and 0.5 respectively.

Probability of India getting points at least 7 in four matches

Let X be the random variable denoting the total points India gets in four matches.

Then, X follows a binomial distribution with n = 4 and p = 0.5.

So, the probability of India getting at least 7 points in four matches is:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

P(X = x) = nCx * px * (1-p)n-x

P(X = 7) = 4C7 * 0.5^7 * 0.5^1 = 0.0625

P(X = 8) = 4C8 * 0.5^8 * 0.5^0 = 0.03125

P(X = 9) = 4C9 * 0.5^9 * 0.5^0 = 0.0078125

P(X = 10) = 4C10 * 0.5^10 * 0.5^0 = 0.0009765625

P(X ≥ 7) = 0.0625 + 0.03125 + 0.0078125 + 0.0009765625 = 0.0875

Therefore, the probability of India getting at least 7 points in four matches is 0.0875, which is option D.
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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, 0.5 and 0.5 respectively. Assuming that the outcomes are independent, the probability of India getting atleast 7 points isa)0.0625b)0.0250c)0.8750d)0.0875Correct answer is option 'D'. Can you explain this answer?
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