Probability Rule
A die is rolled. What is the probability of rolling a 4?
0.167
Flip a coin once. Let X = the number of heads. What are the possible values of X?
x = {0,1}
State the 2 conditions of a valid probability distribution.
1. Each probability is between 0 and 1
2. Total probabilities sum to 1
A card is drawn from a deck. What is the probability it is not a heart?
3/4 or 0.75
Roll a die. Let X = number rolled. List the sample space for X.
Sx = {1, 2, 3, 4, 5, 6}
A coin is flipped once. Construct the probability distribution for X = {0 = tails, 1 = heads}.
x=0 with P=0.5
x=1 with P=0.5
Two coins are flipped. What is the probability of getting at least one head?
3/4 or 0.75
Flip 2 coins. Let X = number of heads. Write the possible values and their probabilities.
Roll a fair die. Construct the probability distribution of X = value rolled.
P(1) = P(2) = ... = P(6) = 1
A bag has 3 red and 2 blue marbles. What’s the probability of pulling a red or a blue marble?
P (red or blue) = 1
Roll two dice. Let X = sum of the dice. What is the probability that x=7?
P(x=7) = 6/36 or 1/6 or 0.167
Flip 2 coins. Show the probability distribution of X = number of heads.
x=0 with P=1/4
x=1 with P= 2/4 or 1/2
x=3 with P=1/4
Two cards are drawn from a deck without replacement. What is the probability both are spades?
P(both spades) = 1/17 or 0.0588
Roll 3 dice. Let X = number of 6’s. What values can X take, and what is the probability of getting exactly 26 sixes?
X = {0, 1, 2, 3}
P(x=2) = (3/2) (1/6)^2 (5/6) = 15/216 = 5/72 = 0.069
A bag contains 3 red and 1 blue marble. One marble is drawn. Show the probability distribution of X = “number of red marbles.”
x=1 (red) with 3/4
x=0 (no red) with 1/4