Sixty- five percent of men consider themselves knowledgeable football fans.
if 10 men are randomly selected, find the probability that exactly six of them will consider themselves knowledgeable fans.

a) 0.65 b) 0.069 c) 0.600 d) 0.238

d) 0.238

Step-by-step explanation:

We would assume binomial distribution for the number of men sampled. The formula for binomial distribution is expressed as

P(x =r) = nCr × q^(n - r) × p^r

Where

p represents the probability of success.

q represents the probability of failure.

n represents the number of samples.

From the information given,

n = 10

p = 65% = 65/100 = 0.65

q = 1 - p = 1 - 0.65 = 0.35

The probability that exactly six of them will consider themselves knowledgeable fans is expressed as P(x = 6). It becomes

P(x =6) = 10C6 × 0.35^(10 - 6) × 0.65^6

P(x =6) = 10C6 × 0.35^4 × 0.65^6

P(x =6) = 0.238

The Converse of Pythagorean Theorem

Step-by-step explanation:

This prove related to The Converse of Pythagorean Theorem, it's a little too long to explain here. Please check your textbook or any reference about this theorem to understand the prove steps.