One of the students is chosen at random. What is the probability that this student is wearing a watch or a braclet

Complete question :

At a certain school, 25% of the students wear a watch and 30% wear a bracelet. 60% of the students wear neither a watch nor a bracelet.

a) One of the students is chosen at random. What is the probability that this student is wearing a watch or a bracelet?

b) What is the probability that this student is wearing both a watch and a bracelet?

0.40 ; 0.15

Step-by-step explanation:

Let :

w = watch

b = bracelet

P(W) = 0.25

P(B) = 0.3

P(either a watch or a bracelet) = P(WuB)

P(neither a watch nor a bracelet) = 1 - P(WuB)

1 - P(WuB) = 0.6

a.) probability that student is wearing a watch or a bracelet = P(WuB)

P(neither a watch nor a bracelet) = 1 - P(WuB)

0.6 = 1 - P(WnB)

P(WnB) = 1 - 0.6

P(WnB) = 0.4

B.) probability that student is wearing both a watch and a bracelet : P(WnB)

Using the probability relation :

P(WuB) = P(W) + P(B) - P(WnB)

0.4 = 0.25 + 0.30 - P(WnB)

0.4 = 0.55 - P(WnB)

P(WnB) = 0.55 - 0.40

P(WnB) = 0.15