Question

Draw two cards from a standard 52-card deck with replacement. Find the probability of getting at least one black card.

Answer 1

Answer:

The value is  $P(s) = \frac{3}{4}$

Step-by-step explanation:

From the question we are told that

  The number of cards in a standard deck of cards is  n = 52

   The number of  black card in a standard deck of cards b = 26

    The number of  non-block cards in a standard deck of cards k =  26

Generally the probability of getting a black card is

           $P(b) = \frac{26}{52}$

=>       $P(b) = \frac{1}{2}$

Generally the probability of getting a non- black card is    

           $P(k) = \frac{26}{52}$

=>       $P(k) = \frac{1}{2}$            

Generally the sample space of the outcome of drawing two card from the  

standard deck of cards in such a way that at least one of the cards is a black card  is  

          $s = \{ bb , bk , kb \}$

Generally the probability of obtaining at least on black card is mathematically represented as

         $P(s) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}$

=>      $P(s) = \frac{1}{4} + \frac{1}{4} + \frac{1}{4}$

=>      $P(s) = \frac{3}{4}$