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Chapter 2: Q. 2.10 (page 48)

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?

Short Answer

Expert verified

a) The probability that the chosen student is wearing a ring or a necklace is0.4

b) The probability that the chosen student is wearing a ring and a necklace is0.1

Step by step solution

01

Part (a) Step 1. Given information.

Using the given information,

Let R be the event that a student is wearing a ring = P(R)=0.20

Let N be the event that a student is wearing a necklace = P(N)=0.30

Students wearing neither a ring nor a necklace =PRc∪Nc=0.60

02

Part (a) Step 2. Find the probability that the chosen student is wearing a ring or a necklace.

The probability that the chosen student is wearing a ring or a necklace is PR∪N.

PR∪N=1-PR∪Nc

According to De-Morgan Law

PRc∪Nc=PR∪Nc

PR∪N=1-0.6=0.4

Therefore, the probability that the chosen student is wearing a ring or a necklace is0.4.

03

Part (b) Step 1. Find the probability that the chosen student is wearing a ring and a necklace.

The probability that the chosen student is wearing a ring and a necklace is P(R∩N).

PR∪N=PR+PN-PR∩N⇒0.4=0.20+0.30-PR∩N⇒PR∩N=0.20+0.30-0.40⇒PR∩N=0.1

Therefore, the probability that the chosen student is wearing a ring and a necklace is0.1.

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