Probability Part 1

Let B1 be the event where Box-I is selected.
& B2→ where box-II selected
P(B1)=P(B2)=

1

2

Let E be the event where selected card is nonprime.
For B1 : Prime numbers :
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
For B2 : Prime numbers :
{31, 37, 41, 43, 47}
P(E)=P(B1)×P(

E

B1

) +P(B2)P(

E

B2

)
=

1

2

×

20

30

+

1

2

×

15

20

Required probability :
P(

B1

E

)=

1 2 × 20 30

1 2 × 20 30 + 1 2 × 15 20

=

2 3

2 3 + 3 4

=

8

17