A. suppose that a single card is selected from a standard 52-card deck. what is the probability that the card drawn is a spade?
b. now suppose that a single card is drawn from a standard 52-card deck, but it is told that the card is black. what is the probability that the card drawn is a spade?

 The required probabilities are

(a) 0.25

(b) 0.5

Step-by-step explanation:  

(a) Given that  a single card is selected from a standard 52-card deck.

We are to find the probability that the card drawn is a spade.

Let S denote the sample space of the experiment of drawing a card and E denote the event that the card drawn is a spade.

Then,

Therefore, the probability of event E is

(b) A single card is drawn from a standard 52-card deck, but it is told that the card is black.

We are to find the probability that the card drawn is a spade.

Let A denote the event that a black card is drawn and B denote the event that the card drawn is a spade.

So,

Therefore, the probability of event B given A is

Thus, the required probabilities are

(a) 0.25

(b) 0.5.

step-by-step explanation:

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