Question

The probability of drawing two white cards without replacement is 14/95, and the probability of drawing one white card is 2/5. What is the probability of drawing a second white card, given that the first card is white?
a. 52/95
b. 7/19
c. 7/38
d. 28/475

Answer 1

A - drawing a white card

B - drawing a secong white card

$P(A)=\dfrac{2}{5}\\ P(A\cap B)=\dfrac{14}{95}\\\\ P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\ P(B|A)=\dfrac{\dfrac{14}{95}}{\dfrac{2}{5}}=\dfrac{14}{95}\cdot\dfrac{5}{2}=\dfrac{7}{19}\Rightarrow \text{B}$