The probability the man will win will be 13.23%. And the probability of winning if he wins by getting at least four heads in five flips will be 36.01%.

<h3>How to find that a given condition can be modeled by binomial distribution?</h3>

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ⁻ˣ⁾

A man wins in a gambling game if he gets two heads in five flips of a biased coin. the probability of getting a head with the coin is 0.7.

Then we have

p = 0.7

n = 5

Then the probability the man will win will be

P(X = 2) = ⁵C₂ (0.7)² (1 - 0.7)⁽⁵⁻²⁾

P(X = 2) = 10 x 0.49 x 0.027

P(X = 2) = 0.1323

P(X = 2) = 13.23%

Then the probability of winning if he wins by getting at least four heads in five flips will be

P(X = 4) = ⁵C₄ (0.7)⁴ (1 - 0.7)⁽⁵⁻⁴⁾

P(X = 4) = 5 x 0.2401 x 0.3

P(X = 4) = 0.3601

P(X = 4) = 36.01%

Learn more about binomial distribution here:

brainly.com/question/13609688

#SPJ1

4 0

2 years ago