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?
Answer:
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
