A two-sided coin (heads/tails) is flipped once, and one card is drawn from a standard 52 deck of playing cards. Calculate the probability of each given situation.

Drawing a King AND drawing a Heart -

Flipping a Heads OR flipping a Tails -

Flipping a Tails AND drawing a King -

Flipping a Tails OR drawing a King -

Drawing a King OR drawing a Heart -

Item bank

1

1/26

1/52

4/13

7/13

Drawing a King AND drawing a Heart - 1/52 Flipping a Heads OR flipping a Tails - 1 Flipping a Tails AND drawing a King - 1/26 Flipping a Tails OR drawing a King - 15/26 Drawing a King OR drawing a Heart - 17/52

Step-by-step explanation:

To solve these we need to understand AND/OR rule of probability.

Simply put "AND" means "multiplication" and "OR" means "addition".

1. Drawing a King AND drawing a Heart:

Pleas note that there are 4 suits in a deck of cards and each suit has 1 king. So in a 52-card standard deck, there is 4 king. Also, there are 13 cards of each suite, so there are 13 hearts out of total 52. Also note that there is "AND" in between (so multiplication).

P (King) * P (heart) = 4/52 * 13/52 = 1/52

2. Flipping a Heads OR flipping a Tails:

Note that there can only be head or tail, so probability of either head of tail is 1/2. Note, there is "OR" in between (so addition).

P (head) + P (tail) = 1/2 + 1/2 = 1

3. Flipping a Tails AND drawing a King:

We already saw the probability of flipping tail is 1/2. Also, we say that there are 4 kings in a standard deck, so probability of drawing a king is 4/52. Note there is "AND" in between (so multiplication). Thus:

P (tails) * P (King) = 1/2 * 4/52 = 1/26

4. Flipping a Tails OR drawing a King

As #3, flipping a tail's probability is 1/2. And, drawing a King's probability is 4/52. BUT here, it is "OR" in between, hence we need to "ADD". Thus:

P (tail) + P (King) = 1/2 + 4/52 = 15/26

5. Drawing a King OR drawing a Heart

As we know, there are 4 suits each with 1 king, so there are total of 4 kings in a standard 52-deck card. Also, there are 13 cards of each suite (hearts, spades, diamonds, clubs). So there are 13 hearts. Hence, probability of King is 4/52 and probability of heart is 13/52. Note that there is "OR" in between, so that means "addition". Thus:

P (king) + P (heart) = 4/52 + 13/52 = 17/52