Question

To maintain their physical fitness, Americans are exercising more than ever in a variety of ways. Bradley and Robbins interviewed many Americans to determine how they were exercising. In How American Exercise, they present the following: 53% jog, 44% swim, 46% cycle, 18% jog and swim, 15% swim and cycle, 17% jog and cycle, and 7% jog, swim, and cycle. If an American who exercises regularly is randomly selected, what is the probability that the person either jogs, swims or cycles to maintain physical fitness?

Do Carefully

Answer 1

here let probability of jog, swin and cycle are P(A),P(B) and P(C) respectively

from above: P(A) =0.53 ; P(B) =0.44 ; P(C)=0.46 ; P(A n B) =0.18 ; P(A C) =0.17 ; P(B n C) =0.15

P(A n B n C )=0.07

hence probability that the person either jogs, swims or cycles to maintain physical fitness

=P(A u B u C) =P(A)+P(B)+P(C)-P(A n B)-P(A n C)-P(B n C) +P(A n B nC)

=0.53+0.44+0.46-0.18-0.17-0.15+0.07 =1.00