Question

A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. (a) The card drawn is 5. The probability is: (b) The card drawn is a face card. The probability is: (c) The card drawn is not a face card. The probability is

Answer 1

Answer:

• a. 1 / 13
• b. 3 / 13
• c. 10 / 13

Step-by-step explanation:

a.

There are four 5's in the deck. This means that, from 52 possible cards to drawn, we have 4 chances of drawing a 5. This means that the probability will be:

$p = \frac{4}{52}$

$p = \frac{1}{13}$

b.

For every suit, there are three face cards, J, Q and K. There are 4 suits, so, the total number of face cards its:

$4 * 3 = 12$

The total possible cards are, still, 52, so, the probability will be

$p = \frac{12}{52}$

$p = \frac{3}{13}$

c.

We know that the card drawn must be a face card, o not being a face card. There is no third choice here. So, the probability of drawing a face card OR not drawing a face car its:

$p = \frac{52}{52} = 1$

so

$p(the \ card \  is \  a \  face  \ card) + p(the \ card \  is \  not \ a \  face  \ card) = 1$

$p(the \ card \  is \  not \ a \  face  \ card) = 1 - p(the \ card \  is \  a \  face  \ card)$

but, we know that

$p(the \ card \  is \  a \  face  \ card = \frac{3}{13}$

so

$p(the \ card \  is \  not \ a \  face  \ card) = 1 - \frac{3}{13}$

$p(the \ card \  is \  not \ a \  face  \ card) = \frac{10}{13}$