# Three cable channels (95, 97, and 103) air quiz shows, comedies, and dramas. There are 14 total quiz shows with channel 95 having 8 and channel 97 having 5. There are 16 comedies with 6 of them...

Three cable channels (95, 97, and 103) air quiz shows, comedies, and dramas. There are 14 total quiz shows with channel 95 having 8 and channel 97 having 5. There are 16 comedies with 6 of them appearing on channel 103. There are 5 dramas on channel 95 and 2 dramas on channel 97. Channel 97 has 15 total shows while channel 103 has 14 total shows. All together there are 44 different shows. What is the probability that a show is on channel 103 or it is a comedy?

justaguide | Certified Educator

Three cable channels (95, 97, and 103) air quiz shows, comedies, and dramas.

There are 14 quiz shows in all with channel 95 having 8 and channel 97 having 5. One quiz show is aired on channel 103.

There are 16 comedies with 6 of them appearing on channel 103.

Channel 103 has 14 show in all of 6 are comedies.

The number of shows that are either a comedy or are aired on channel 103 are `N(C) + N(103) - N(Cuu103) = 16 + 14 - 6 = 24` .

The total number of shows on all the three channels is 44.

This gives the probability that a show is either a comedy or is aired on channel 103 as `24/44 = 6/11`

The required probability is 6/11