Ten asthmatics were asked to compare the effect of salbutamol and fenoterol sprays in relieving their asthma attacks. Assume that salbutamol and fenoterol are equal in terms of effectiveness and side effects in all people, so that the preferences expressed are simply the reflection of a 50-50 random choice.

a. With this assumption, what is the probability that (i) zero people prefer fenoterol to salbutamol? (ii) one prefers fenoterol? (iii) two prefer fenoterol? (iv) three prefer fenoterol? (v) four prefer fenoterol? (vi) five prefer fenoterol?

b. How low would the number prefering fenoterol to salbutamol have to be before you would believe that the results are not simply due to random chance but that salbutamol is a better drug? (Note there is no "right" answer.) POLI967