Question

1. drawing a card if a card is drawn from a deck, find the probability of getting these results:

a. a 6 and a spade
b. a black king
c. a red card and a 7
d. a diamond or a heart
e. a black card

Explanation:

Step1: Define total card count

A standard deck has $n(\text{Total}) = 52$ cards.

Step2: Solve part (a): 6 and spade

There is 1 card that is both a 6 and a spade.
Probability: $\frac{n(\text{6 and spade})}{n(\text{Total})} = \frac{1}{52}$

Step3: Solve part (b): Black king

There are 2 black kings (spade king, club king).
Probability: $\frac{n(\text{Black king})}{n(\text{Total})} = \frac{2}{52} = \frac{1}{26}$

Step4: Solve part (c): Red card and 7

There are 2 cards that are red and a 7 (heart 7, diamond 7).
Probability: $\frac{n(\text{Red and 7})}{n(\text{Total})} = \frac{2}{52} = \frac{1}{26}$

Step5: Solve part (d): Diamond or heart

There are 13 diamonds and 13 hearts, no overlap.
$n(\text{Diamond or heart}) = 13 + 13 = 26$
Probability: $\frac{26}{52} = \frac{1}{2}$

Step6: Solve part (e): Black card

There are 26 black cards (13 spades, 13 clubs).
Probability: $\frac{26}{52} = \frac{1}{2}$

Answer:

a. $\frac{1}{52}$
b. $\frac{1}{26}$
c. $\frac{1}{26}$
d. $\frac{1}{2}$
e. $\frac{1}{2}$