Question

A nonprofit organization conducted a survey of 2080 metropolitan-area teachers regarding their beliefs about problems that hamper students' schooling. The following data were obtained.

860	said that lack of parental support is a problem.
860	said that abused or neglected children are problems.
670	said that malnutrition or students in poor health is a problem.
100	said that lack of parental support and abused or neglected children are problems.
90	said that lack of parental support and malnutrition or poor health are problems.
140	said that abused or neglected children and malnutrition or poor health are problems.
20	said that lack of parental support, abuse or neglect, and malnutrition or poor health are problems.

What is the probability that a teacher selected at random from this group said that lack of parental support is the only problem hampering students' schooling? Hint: Draw a Venn diagram. (Round your answer to three decimal places.)

Answer 1

Let P denote lack of parental support and

Let N denote abused or neglected children and

Let M denote malnutrition or students in poor health

Then from the given details we can write

n(P)= 860, n(N) = 860, n(M) = 670 ,n(PN) = 100, n(PM) =90, n(NM) = 140, n(NPM) = 20.

A Venn diagram can be drawn using the given details and is drawn below:

Now we need to find the probability that a teacher selected at random from this group said that lack of parental support is the only problem hampering students' schooling. And the required region is marked in the following diagram.

Thus, number students lacking parental support is the only problem hampering students' schooling  

  

= 690.

Hence probability that a teacher selected at random from this group says that students lacking parental support is the only problem hampering students' schooling is: 690/2080 = 0.3317= 0.332