A hat contains a number of cards with 30% white on both sides, 50% black on one side and whit e on the other side, 20% black on both sides. The cards are mixed up, and a single card is drawn at random and placed on the table. Its upper side shows up black. The probability that its other side is also black is `2//9` b. `4//9` c. `2//3` d. `2//7`

Options

A. `2//9`
B. `4//9`
C. `2//3`
D. `2//7`

Answer

B

Explanation

Let us consider the following events.
A: card shows up black
`B_(1):` card with both side black
`B_(2):` card with both sides white
`B_(3),` card with one side white and one black

`P(B_(1))=2/10,P(B_(2))=3/10,P(B_(3))=5/10`
`P(A//B_(1))=1,P(A//B_(2))=0,P(A//B_(3))=1/2`
`P(B_(1)//A)=(2/10x1)/(2/10x1+3/10xx(0)+5/10xx1/4)=(4)/(4+5)=4/5`