I got stuck on this question while tutoring a Math 12 student :
Q : There are 12 boys and 10 girls in a class. A yearbook committee of 4 is to be chosen at random. What is the probability (to the nearest 1/100th) that the committee is made up of Ryan (school president) and 3 girls?
A : The official answer says 0.2
I'm not sure if I'm calculating this correctly, my answer is :
(10C3 + 12C1) / (22C4) = (120 + 12) / 7315 = 0.0180 (which can be rounded up to 0.02)
Q : (b) if Ryan has to be on the committee, what is the probability that 3 girls are chosen?
A : The official answer says 0.09
I don't see how this is different from the previous question???
My best guess would be :
10C3 / 21C3 = 120 / 1330 = 0.0902 (which can be rounded up to 0.09)
I think the wording is what has confused me the most here, any advice/suggestions would be greatly appreciated!