The probability is 0.1932 that a randomly selected man considers himself a professional fan.
<h3>What is probability?</h3>
Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
We have been given data as:
The number of randomly selected men, n = 10.
Probability of success, that a randomly selected man considers himself a professional fan, p = 61% or 0.61
Probability of failure, that a randomly selected man does not consider himself a professional fan is:
⇒ q = 1 − p = 1 − 0.61= 0.39
The probability that the number of men who consider themselves professional fans is:
⇒ ⁿcₓpˣqⁿ⁻ˣ
Substitute exactly x = 5
⇒ ¹⁰c₅(0.61)⁵(0.39)¹⁰⁻⁵
⇒ ¹⁰c₅(0.61)⁵(0.39)⁵
⇒ 0.1932
Therefore, the required probability is 0.1932.
Learn more about the probability here:
brainly.com/question/11234923
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