Answer:
[tex]\frac{1}{17}[/tex]
Explanation:
Let D be the event that the lost card is a diamond
and D' be the event that the lost card is a non diamond
Therefore,
P(D) = [tex]\frac{13}{52}[/tex] = 0.25
P(D') = [tex]\frac{39}{52}[/tex] = 0.75
Now,
Event that the cards picked up are both diamonds = A
Thus,
P( A | D) = [tex]\frac{12}{51 }\times\frac{11}{50}[/tex] [ As One Diamond Card is lost ]
And,
P(A | D') = [tex]\frac{13}{51}\times\frac{12}{50}[/tex] [ As One Non-Diamond card is lost ]
Therefore,
P(A) = P(D) × P(A | D) + P(D') × P( A | D')
= 0.25 × [tex]\frac{12}{51 }\times\frac{11}{50}[/tex] + 0.75 × [tex]\frac{13}{51}\times\frac{12}{50}[/tex]
= [tex]\frac{1}{17}[/tex]
