3. The Indian cricket team is visiting New Zealand to play a test series comprising five...

3. The Indian cricket team is visiting New Zealand to play a test series comprising five matches. In each match, assume that the Indian team has a 70% chance of winning. Further, assuming that the matches are independent of each other, what is the probability that:

a. The Indian team will win the series?

b. The team will win all five matches, and that the team will lose all?

Solutions

Expert Solution

Solution: We are given:

Let x be the number of matches won by the Indian team

a. The Indian team will win the series?

Answer: The Indian team will win the series only if they win three or more matches. Therefore, we have to find:

Using the binomial probability distribution, we have:

Therefore, the Indian team will win the series is 0.8369

b. The team will win all five matches, and that the team will lose all?

The probability that the Indian team will win all five matches is:

Therefore, the probability that the Indian team will win all five matches is 0.1681

The probability that the Indian team will lose all five matches is:

Therefore, the probability that the Indian team will lose all five matches is 0.0024

orchestra answered 1 year ago

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