Question

Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1/52 probability. How many sample points are there in the event that a king is selected? How many sample points are there in the event that a diamond is selected? How many sample points are there in the event that a non face card (non jack, non queen, or non king) is selected? Find the probabilities associated with each of the events in parts (a), (b), and (c) (to 2 decimals). (a) Ace (b) Club (c) Non face card

Answer 1

Answer:

A) 4, 13, 40

B) a) 0.07 b) 0.25 c) 0.77

Step-by-step explanation:

We are given the following in the question:

Number of cards in a deck  = 52

Sample points are there in the event that a king is selected

= Number of kings in a deck of card = 4

Sample points are there in the event that a diamond is selected

= Number of diamond card in a deck of card = 13

Sample points are there in the event that a non face card

= Number of non-face card in a deck of card = 52-12 = 40

Formula:

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

(a) Ace

$P(Ace) = \dfrac{4}{52}=\dfrac{1}{13} = 0.07$

(b) Club

$P(Club) = \dfrac{13}{52} = \dfrac{1}{4} = 0.25$

(c) Non face card

$P(\text{Non face card}) = \dfrac{40}{52} = \dfrac{10}{13} = 0.77$

Answer 2

Answer:

(A) Sample points in the event that a king is selected = 4

     Sample points in the event that a diamond is selected = 13

     Sample points in the event that a non face card = 40

(B) (a) 0.08     (b) 0.25       (c) 0.77

Step-by-step explanation:

We are given that Consider the experiment of selecting a playing card from a deck of 52 playing cards. Also, each card corresponds to a sample point with a 1/52 probability.

Now, Sample points in the event that a king is selected = 4 because there are 4 kings in the deck of 52 cards.

Sample points in the event that a diamond is selected = 13 because there are 13 diamonds in the deck of 52 cards.

Sample points in the event that a non face card (non jack, non queen, or non king) = There are 12 face cards in the deck of 52 cards so non face cards = 52 - 12 = 40 non face cards.

Now, Probability of any event = Favorable outcomes ÷ Total outcomes

(a) Number of Ace cards in the deck of 52 cards = 4 {2 black & 2 red}

    Number of total cards in a deck = 52 cards

So, Probability of Ace card = $\frac{4}{52}$ = 0.08

(b) Number of Club cards in the deck of 52 cards = 13

    Number of total cards in a deck = 52 cards

So, Probability of Club card = $\frac{13}{52}$ = 0.25

(c) Number of Non face cards in the deck of 52 cards = 52 - 12 = 40

    Number of total cards in a deck = 52 cards

So, Probability of Non face card = $\frac{40}{52}$ = 0.77