Question

Sick children: There are 21 students in Mrs. Bush's sixth-grade class. On a cold winter day in February, many of the students had runny noses and sore throats. After examining each student, the school nurse constructed the following table. Round the answers to four decimal places, as needed. 

	Sore Throat	No Sore Throat
Runmy Nose No Runny	6	8
Nose	2	5

(a) Find the probability that a randomly selected student has a runny nose. 

(b) Find the probability that a randomly selected student has a sore throat. 

(c) Find the probability that a randomly selected student has a runny nose or a sore throat. 

(d) Find the probability that a randomly selected student has neither runny nose nor a sore throat.

Answer 1

Answer 2

SOLUTION :

a.

P(Runny nose) 

= N(runny nose) / N(total students)

= 14/21

= 2/3 (ANSWER).

b.

P(Sore Throat) 

= N(Sore throat) / N (Total students)

= 8 / 21 (ANSWER).

c.

P(Runny nose or Sore throat)

= P(Runny nose) + P(sore throat) - P(Runny nose and Sore throat)

= 2/3 + 8/21 - 6/21

= 16/21 (AANSWER).

d.

P(Nether Runny nose nor a sore throat)

= P(no runny nose) + P(no sore throat) - P(no runny nose and no sore throat)

= 7/21 + 13/21 - 5/21

= 15/21

= 5/7 (ANSWER).