MATH SOLVE

2 months ago

Q:
# 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 bank1 1/261/524/137/13

Accepted Solution

A:

Answer: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 - 17/52Step-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 = 1/522. 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 = 13. 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 = 1/264. Flipping a Tails OR drawing a KingAs #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 = 15/265. Drawing a King OR drawing a HeartAs 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