A coin is tossed once. What is the probability of the coin coming up "tails"?
The coin can come up with either :
"heads" (H) or "tails" (T)
Thus, the set S of possible outcomes is
S = {H, T}
\[\therefore P(T) = \frac{1}{2}\]
What is the probability of getting an even number in a single throw of dice?
Clearly, a die can fall with any of its uppermost faces.
The number on each of the faces is, therefore, a possible outcome. Thus, there are total 6 outcomes.
Since there are 3 even numbers on the die, namely :
2, 4, 6.
\[\therefore P(\text{even number}) = \frac{3}{6} = \frac{1}{2}\]
What is the probability of drawing a 'king' from a well-shuffled deck of 52 cards?
Well-shuffled ensures equally likely outcomes.
There are 4 kings in a deck.
\[\therefore P(\text{a King}) =\frac{4}{52} = \frac{1}{13}\]
A card is drwan at random from a well-shuffled pack of 52 cards. Find the probability of getting a jack or a queen or a king.
P (a jack or a queen or a king)
= P(a jack) + P(a queen) + P(a king)
\[=\frac{4}{52}+\frac{4}{52}+\frac{4}{52}\]
\[=\frac{1}{13}+\frac{1}{13}+\frac{1}{13}\]
\[=\frac{3}{13}\]
A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of getting a two of heart or diamond.
P (two of heart or diamond)
= P(two of heart) + P(two of diamond)
\[=\frac{1}{52}+\frac{1}{52}\]
\[=\frac{2}{52}\]
\[=\frac{1}{26}\]
From a well-shuffled pack of 52 cards, a card is drawn at random, find the probability that it is either a heart or a queen.
Let us suppose that
Then, the probability of getting -
either a heart H or queen Q
\[= P\left(H\cup Q\right)\]
\[=P\left(H\right)+P\left(Q\right)-P\left(H\cap Q\right)\]
\[=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\]
\[=\frac{16}{52}\]
\[=\frac{4}{13}\]