Question

CH NEXT Chapter 04, Section 4.4 Problem 056 x Incorrect In a statistics class of 52 students, 27 have volunteered for community service in the past. If two students are selected at random from this class, what is the probability that both of them have volunteered for community service? Round your answer to four decimal places. 0.5192 Pboth students have volunteered for community service) the absolute tolerance is +/-0.0005

Answer 1

Among 52 students in the class, 27 had volunteered for community services.

Now, we can randomly select two students from the class in

ways .

52 52! 250!

Our required case is that both of them had volunteered for community service. For that to happen we have to choose from the 27 students who volunteered. Similarly here it can be done in $\tiny \binom{27}{2} = \frac{27!}{2!25!}$ ways.

Thus the required probability is

$\frac{\frac{27!}{2!25!}}{\frac{52!}{2!50!}}= \frac{27*26}{52*51}=\frac{3*9}{2*17*3}=0.2647$