Sixty percent of the students at a certain school wear

Chapter 2, Problem 10P

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QUESTION:

Sixty percent of the students at a certain school wear neither a ring nor a necklace. Twenty percent wear a ring and 30 percent wear a necklace. If one of the students is chosen randomly, what is the probability that this student is wearing

(a) a ring or a necklace?

(b) a ring and a necklace?

Questions & Answers

QUESTION:

Sixty percent of the students at a certain school wear neither a ring nor a necklace. Twenty percent wear a ring and 30 percent wear a necklace. If one of the students is chosen randomly, what is the probability that this student is wearing

(a) a ring or a necklace?

(b) a ring and a necklace?

ANSWER:

Step 1 of 2

(a)

We are asked to find the probability that randomly chosen student is wearing a ring or a necklace.

Let  be the event that a student wears a ring.

Let  be the event that a student wears a necklace.

We need to find

The probability that a student wears a ring is,

                         

The probability that a student wears a necklace is,

                         

We have given that sixty percent of the students wear neither a ring nor a necklace.

The probability that a student wears neither a ring nor a necklace is,          

             

The probability that randomly chosen student is wearing a ring or a necklace is,

                 

                 

Hence the probability that randomly chosen student is wearing a ring or a necklace is

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