Answer to Question #193147 in Statistics and Probability for Daniela(me)

Question

 

16. For each of the following, write the probability in symbolic form and give the answer. 

a) The probability that a female student is in the band but does not have a drivers’ license. 

    

b) The probability that a female student has a drivers’ license but is not in the band. 

     

c) The probability that a female student is not in the band and does not have a drivers’ license. 

     

d) The probability that a female student is in the band or has a drivers’ license. 

Answer 1

Let $B$ be the event that a female student is in the band, $D$ be the event that a female student has a drivers’ license.

a) The probability that a female student is in the band but does not have a drivers’ license

$$P(B\cap D')$$

b) The probability that a female student has a drivers’ license but is not in the band. 

$$P(B'\cap D)$$

c) The probability that a female student is not in the band and does not have a drivers’ license. 

$$P(B'\cap D')$$

d) The probability that a female student is in the band or has a drivers’ license. 

$$P(B\cup D)$$