SOLUTION: 4. The probability that an adult male is shorter than 66 inches is 0.3; that he is between 66 and 70 inches is 0.5; and that he is taller than 70 inches is 0.2. If two males ar

Algebra ->  Probability-and-statistics -> SOLUTION: 4. The probability that an adult male is shorter than 66 inches is 0.3; that he is between 66 and 70 inches is 0.5; and that he is taller than 70 inches is 0.2. If two males ar      Log On


   

Question 339740: 4. The probability that an adult male is shorter than 66 inches is 0.3; that he is between 66 and 70 inches is 0.5; and that he is taller than 70 inches is 0.2. If two males are picked at random, find the probability that:

a. the heights of both are between 66 and 70 inches.


b. the first is shorter than 66 inches and the second is taller than 70 inches.


c. the first is 70 inches or shorter and the second is 66 inches or taller.

Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
a. Probability the heights of both are between 66 and 70 inches
P((both between 66 and 70)=P%2866%3Cx%3C70%29P%2866%3Cy%3C70%29=0.5%2A0.5=0.25
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b. probability the first is shorter than 66 inches and the second is taller than 70 inches.
P(x<66 and y>70)=P(x<66)P(>70)=0.3*0.2=0.06
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c. probabilitythe first is 70 inches or shorter and the second is 66 inches or taller
P(x<70 and y>66)=P(x<70)P(>66)=(0.3+0.5)*(0.5+0.2)=0.8*0.7=0.56