Bob does not do his survey every day, as sometimes he decides it's too hot. If it's 32 degrees or more, then Bob will only go outside and conduct his survey with probability 0.1, while if it is under 32 degrees then Bob will go outside and conduct his survey with probability 0.6. Let x be the probability that it is over 32 degrees. Let H denote the event that it's hot (ie 32 degrees or over) and S denote the event that Bob conducts his survey. Obtain an equation for P(S) in terms of x. Please demonstrate (and label) the use of the law of total probability and the multiplication rule in your working out