A grade 11 art class is offering students two choices for a project: a pottery project and a mixed media project. Of the 46 students in the class, 23 have selected to do the pottery project and 33 have selected to do the mixed media project (notice some students have decided to do both) It two students are selected at random from the class to show their finished project(s), what is the probability that at least one pottery project and at least one mixed media project will be shown? Probability (given to three decimal places)

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if i read the problem correctly this means ten have done both, 13 have chosen pottery only and 23 have chosen mixed media only does that seem right?

lets assume that it is then lets compute the probability that the desired result is not true, that is, compute the probability that only one activity is represented the probability that there are both potter only is \[\frac{13}{46}\times \frac{12}{45}\] the probability that they are both mixed media only is \[\frac{23}{46}\times \frac{22}{45}\] since these are disjoint event, the probability of one or the other is their sum, that is \[\frac{13}{46}\times \frac{12}{45}+\frac{23}{46}\times \frac{22}{45}\] find this number and subtract the result from one

yes that makes sense okay i will try to calculate it :)

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