A
You toss two fair coins. Let X be the number of heads. Find: The probability distribution of X.
Outcomes: HH, HT, TH, TT
P(X=0)=1/4
P(X=1)=2/4
P(X=2)=1/4
Pick a number randomly from the set {1, 2, 3, 4, 5}. Let X=1X = 1X=1 if even, X=0X = 0X=0 if odd.
Find: The probability distribution.
Even: {2, 4} → 2 numbers
Odd: {1, 3, 5} → 3 numbers
P(X=1)=2/5
P(X=0)=3/5
You toss a fair coin once.
Let X=1 if heads, X=0 if tails.
Find: Probability distribution of X
P(X=1)=0.5, P(X=0)=0.5
You roll a fair 6-sided die. Let X be the number shown on the die.
Find: The probability that X=4.
1/6
A bag contains 3 red balls and 2 blue balls. One ball is picked at random.
3/5 red
2/5 blue
Let Х be the number of heads in 3 coin tosses.
Find: Probability distribution of X.
Possible values: 0, 1, 2, 3
P(X=0)=1/8
P(X=1)=3/8
P(X=2)=3/8
P(X=3)=1/8
You roll two fair dice. Let X be the sum.
Find: The probability that X=7.
There are 6 outcomes that give 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
P(X=7)=6/36=1/6
You toss a coin and roll a die.
Find: The probability of getting heads and a number greater than 4.
Coin: Heads = 0.5
Die > 4: {5,6} → 2/6=1/3
P=0.5⋅(1/3)=1/6
Flip a coin and roll a die. What is the probability that you do not get heads or do not roll a 1?
Total outcomes: 12
Only 1 "bad" outcome: (Heads, 1)
P(not heads or not 1)=1−P(heads and 1)=1−(1/2⋅1/6)=1−1/12=11/12