Question

without replacement two cards are drawn at random from a pack of 52 cards with what probability can you say that both cards are black

Answer 1

50% the probability will be 50% or 1/2 or 0.5

Answer 2

Answer:

Probability is $\frac{25}{102}$

Step-by-step explanation:

If A and B are independant events then

P ( A ∩ B ) = P( A ) * P( B )

Since we know,

In a pack of 52 cards, there are 26 black cards.

If A is the event that a black card is drawn, then

P(A) = $\frac{26}{52}$

= $\frac{1}{2}$

After drawing one black card, there will  25 black card left in the packet and

Total number of cards will be 51 now

Let B be the event of drawing a black in the second draw,

then P(B) = $\frac{25}{51}$

Since A and B are independent events,

P( A ∩ B ) = P ( A ) * P ( B )

⇒P( A ∩ B ) = P ( both cards are black )

$\frac{1}{2}$ *  $\frac{25}{51}$ = $\frac{25}{102}$

Hence,

Probability is $\frac{25}{102}$