Two cards are drawn successively without replacement from a well-shuffled deck of cards

MATHEMATICS · Single correct · CBSE · Mathematics · Probability · Probability

Problem

Two cards are drawn successively without replacement from a well-shuffled deck of

52

cards. Let

A

be the event that the first card is a spade and

B

be the event that the second card is a spade. Which statement about the events

A

and

B

is correct? (a)

A

and

B

are mutually exclusive since once a spade has been drawn first, it cannot appear again as the second card. (b)

A

and

B

are not independent because removing one card changes the sample space for the second draw. (c)

A

and

B

are independent because

P(B)=\dfrac{13}{52}

in every case. (d)

A

and

B

are independent because

P(A\cap B)=\dfrac{13}{52}\times\dfrac{13}{52}