Question

a box contains 50 bolts and 150 nuts. on checking the box, it was found that half of the bolts and half of the nuts are rusted. if one of them is chosen at random, find the probability that it is rusted

Answer 1

Number of bolts = 50

Number of nuts = 150

total tools = 150 + 50 = 200

Rusted bolts = 25

Rusted nuts = 75

P(one of them is rusted) = 25 + 75 / 200 = 100/200 = 1/2

Answer 2

P(A)= item chosen is rusted

=  

200

100

​  

=  

2

1

​  

 

P(B)= item chosen is bolt =  

200

50

​  

=  

4

1

​  

 

P(A∩B)= item is rusted and bolt =  

200

25

​  

=  

8

1

​  

 

P(A∪B)= prob. of item is rusted or bolt

=P(A)+P(B)−P(A∩B)

=  

2

1

​  

+  

4

1

​  

−  

8

1

​  

=  

8

5

​ ​