The table blow lists the number of three kinds of television shows aired on thre
ID: 3200634 • Letter: T
Question
The table blow lists the number of three kinds of television shows aired on three channels. If a viewer selects anyone of these shows at random find he following: ( Assume that each show on any one of the listed channels is equally likely to be aired at any give time).
a. A drama or comedy was viewed
b.a show on channel 7 was viewed
c. A comdey or channel 13 was selected and viewed
d. a drama was viewed given that channel 4 was selected
channel 4 channel 7 channel 13 daram 9 13 5 comedy 6 5 7 quiz show 7 9 10Explanation / Answer
a) Probability of selecting any cgannel = 1/3
P(D4) = 9/22 , P( D7) = 13/27 , P(D13) = 5/22
P(C4) = 6/22 , P( C7) = 5/27 , P(C13) = 7/22
Probability of drama 0r comedy on channel 4 = 1/3 ( 9/22 + 6/22)
= 5/22
Probability of drama 0r comedy on channel 7 = 1/3 ( 13/27 + 5/27)
= 2/9
Probability of drama 0r comedy on channel 13 = 1/3 ( 5/22 + 7/22)
= 2/11
Total Probability = 5/22 + 2/9 + 2/11 = 0.63
b) Probability of selecting a show on channel 7 = 1/3
c) Probability of selecting a comedy P(C) = 1/3 * (6/22 + 5/27 + 7/22) = 0.258
Probability of selecting a channel13 P(C13) = 1/3
P( C intersection C13) = 1/3 * 5/27 = 0.061
P( C union C13) = P(C) + P(C13) - P( C intersection C13)
= 0.258 + 0.333 - 0.061
= 0.530
d) Probability of selecting a drama on channel 4 P( D|C4) = P(D intersection C4) / P(C4)
= (1/3 * 9 /22) / 1/3
= 9/22 = 0.409
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