Posted by Anonymous on Wednesday, June 27, 2012 at 1:15pm.
Sara tossed a fair coin five times, and Kaleb tossed a fair coin three times. There were five heads and three tails in the eight tosses. What is the probability that either Sara or Kaleb tossed exactly three heads? Express your answer as a common fraction.

common fraction  Count Iblis, Wednesday, June 27, 2012 at 4:23pm
Probability that Sarah throws exactly 3 heads:
Binomial[5,3] 2^(5) = 10/32 = 5/16
Probability that Sarah does not throw excatly 3 heads is:
1  5/16 = 11/16
Probability that Kaleb throws exactly 3 heads:
1/8
Probability that Kaleb does not throw excatly 3 heads is:
11/8 = 7/8
Probability that neither Kaleb nor Sarah throw exactly 3 heads is:
11/16 * 7/8 = 77/128
Probability that either Kaleb or Sarah throw exactly 3 heads is:
1  77/128 = 51/128