But how sure is 'very sure'? 99% sure? Having 72 seats wouldn't make you 99% sure ...... (in fact, it would only make you about 53% sure!).
Let X be the random variable number of non-smoking seats required.
Then X ~ Binomial (n = 120, p = 0.6)
To be say, 99% sure, you need to find the smallest value of x such that . This value of x is the number of seats required.
You can use technology to very easily solve for x ..... I get x = 84.