A survey revealed that 44% of people are entertained by reading books, 46% are entertained by watching TV, and 10% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV?

3 Answers

#8/10 = 4/5 = .8#

Explanation:

Let total surveyed people be #x#.
We are given that #10%# #i.e. (10x)/100 # people are
entertained by both TV and books.

Since #44%# #i.e. (44x)/100# people are entertained by books.
#therefore # the number of people entertained ONLY by books is given by:-

#(#number of people entertained by books#)## -# #(#number of people entertained by BOTH books and TV#)#
#= (44x)/100 - (10x)/100 = (34x)/100#

Similarly,

Since #46%# #i.e. (46x)/100# people are entertained by books.
#therefore # the number of people entertained ONLY by TV is given by:-

#(#number of people entertained by TV#)## -# #(#number of people entertained by BOTH books and TV#)#
#= (46x)/100 - (10x)/100 = (36x)/100#

#therefore# number of people entertained by EITHER books or TV:-
#=##(#number of people entertained ONLY by books#)# #+# #(# number of people entertained ONLY by TV #)# #+# #(#People entertained by both TV and books #)#

#= (34x)/100 + (36x)/100 + (10x)/100 = (80x)/100#

#hence,# probability that a person will be entertained by either books or TV #=#
(number of people entertained by EITHER books or TV)#/#(total number of people surveyed)

#= ((80x)/100)/x = 8/10 = 0.8#

Apr 12, 2017

#P#(books or TV) =#4/5#

Explanation:

The numbers that are given only tell us about the people who are entertained by books and TV only, but not about other forms of entertainment.

The #44%# of people who read includes the #10%# who read and watch TV. Therefore we can deduce that #34%# of the people are entertained by ONLY books.

In the same way, the people who ONLY watch TV make up #46%-10% =36%#

Now we have the information that of people surveyed:

Only books = #34%#
Only TV = #36%#
Books and TV = #10%#

This makes up #34%+36%+10% =80%# of people surveyed.

There are therefore #20%# who have other forms of entertainment.

The probability that a person is entertained by books or TV :

#P= 80/100 = 4/5#

Apr 13, 2017

# 4/5=80%.#

Explanation:

Let, #B=# the Event that a person is entertained by reading Books,

#T=# the event that a person is entertained by watching TV.

Then, #BuuT=# the event taht a person is entertained by either

books or TV; and,

#BnnT=# the event taht a person is entertained by both the means.

By what is given, we have,

#P(B)=44/100, P(T)=46/100, & P(BnnT)=10/100.#

#:." The Reqd. Prob="P(BuuT)=P(B)+P(T)-P(BnnT),#

#=(44+46-10)/100=80/100=4/5=80%.#

Enjoy Maths.!