Question

a card is drawn at random from a well shuffled pack of 52 cards find the probability that the card drawn is neither a black card nor a king?

Answer 1

P( Picking a card which is neither a black card nor a king ) = 6/13

Explanation:

Let E : Event of drawing a card which is either black card or a king.

So, the number of favorable outcomes = { 2 Red King, 26 black cards spades} = 28

Now,
`\textrm{P(E)}  = \frac{\textrm{Total number of favorable outcomes}}{\textrm{Total number of outcomes}}`

or,
`P(E) = (28)/(52)   = ((7)/(13) )`

⇒P(Picking a picking a card which is either black or a king ) = 7/13

Now, P(not E) = 1 - P(E)

⇒P( not Picking either black card or a king ) = 1 - P(Picking a picking a card which is either black or a king )

=
`1- (7)/(13)   = (13 - 7)/(13)   = ((6)/(13))`

⇒P( not Picking either black card or a king ) = 6/13

or, P( Picking a card which is neither a black card nor a king ) = 6/13