Question

Six cards are identical except that both sides of two cards are red, both sides of three cards are black, and the sixth card has one red side and one black side. One of the six cards is chosen at random and placed on a table. If the upper side of the chosen card is red, what is the probability that the bottom side is black?

Answer 1

Answer 2

PAGE A Upper side of the card is rech B » Bottom side of the card is black we have tu find (BIA) -P(BIA) Poneiside of the card is black given that one side of the card is. Ques bready red) let A) B - om side of One sich of the and is reat the card is black P(BIA) P CAOB). PLA) PCARB) = Plone side is red & one she is black) 6 PLAY Plone side of the card is red) 3 6 2 R( BLAJ- 6 2 12

Answer 3

There are three groups of cards
Both side Red: (R-R) - 2 cards. Probability of selecting this group is 2/6 = 1/3
Both side Black: (B-B) - 3 cards. Probability of selecting this group is 3/6 = 1/2
One side Red and One Black : (R-B) - 1 cards. Probability of selecting this group is 1/6.
If we select card from the first group, then probability that the upper face is red is 1.
If we select card from the second group, then probability that the upper face is red is 0.
If we select card from the third group, then probability that the upper face is red is 1/2.

Using conditional probability,

$P(\textrm{bottom is black/upper is red})=\frac{\frac{1}{6}\times \frac{1}{2}}{\frac{2}{6}\times 1+\frac{3}{6}\times 0+\frac{1}{6}\times \frac{1}{2}}=\frac{1}{5}$

Answer 4

PCB/R) P(R/B) P(B) PLR/B) PCB) P(R/R) P(R) (6) = - = 3 (6)+( 6

Answer 5

PAGE A Upper side of the card is rech B » Bottom side of the card is black we have tu find (BIA) -P(BIA) Poneiside of the card is black given that one side of the card is. Ques bready red) let A) B - om side of One sich of the and is reat the card is black P(BIA) P CAOB). PLA) PCARB) = Plone side is red & one she is black) 6 PLAY Plone side of the card is red) 3 6 2 R( BLAJ- 6 2 12