Respuesta :
The probability that the islanders will win exactly two games is 0.359.
How to find probability using binomial distribution?
The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Given that,
The probability of winning is 4/7.
Then the probability to lose is 1 - 4/7 = 3/7.
If islanders win exactly two games out of four, it implies that they will lose 2 as well.
Now, the probability of winning exactly two games can be found using binomial distribution as given below,
⁴C₂(4/7)²(3/7)²
= 6 × 16/49 × 9/49
= 864/2401
= 0.359
Hence, the probability of winning exactly two games is 0.359.
To know more about binomial distribution click on,
https://brainly.com/question/14565246
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