Coin & Dice
Probability of flipping a coin and getting heads.
1/2
Probability of drawing a heart from a standard deck.
13/52 = 1/4
Probability of picking a blue marble from a bag with 3 blue and 2 red marbles.
3(3+2) = 3/5
Probability of rolling a die twice and getting 2 sixes
1/6 x 1/6 = 1/36
A bag has 5 candies: 2 chocolate, 3 strawberry. Pick 1 candy. What is the probability it is chocolate?
2/5
Probability of rolling a 6 on a standard die.
1/6
Probability of drawing a king from a standard deck.
4/52 = 1/13
Probability of picking a number 4 from (1,2,3,4,5).
1/5
Probability of picking 2 red marbles with replacement from a bag with 4 red and 6 blue marbles.
4/10 x 4/10 = 16/100 = 4/25 (with replacement)
There are 3 green shirts and 7 red shirts. Pick 1 shirt at random. Probability it is green?
3/10
Probability of rolling an even number on a die.
Probability of drawing a red card or a queen.
Red cards: 26/52, Queens: 4/52. Red queen counted once > 26+4-1=29? Wait carefully: Red cards include 2 red Queens, not 1. Actually 26 red + 2 black Queens = 28/52 = 7/13
Probability of rolling a number less than 3 on a die.
Number less than 3: 1,2 > 2/6 = 1/3
Probability of drawing a red card then a black card without replacement.
26/52 x 26/51 = 13/51
A spinner has 4 equal sections labeled 1,2,3,4. Probability of spinning a 3?
1/4
Probability of flipping 2 coins and getting both heads.
1/2 x 1/2 = 1/4
Probability of drawing 2 aces in a row without replacement.
4/52 x 3/51 = 12/2652 = 1/221
Probability of flipping a coin twice a and getting exactly one head.
HT, TH > 2/4 = 1/2
Probability of rolling a sum of 5 or 6 on two dice.
Sum 5: (1,4), (2,3), (3,2), (4,1) > 4
Sum 6: (1,5), (2,4), (3,3), (4,2), (5,1) > 5
9/36 = 1/4
A die is rolled twice. Probability the first roll is odd and second is even?
First odd: 3/6 = 1/2; Second even: 3/6 = 1/2 -> 1/2 x 1/2 = 1/4
Probability of rolling two dice and getting a sum of 7
6/36 = 1/6 (pairs: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1)
Probability of drawing a face card (Jack, Queen, King)
12/52 = 3/13
Probability of picking an odd number from (1,2,3,4,5,6,7,8,9).
Odd numbers : 1,3,5,7,9 > 5/9
Probability of flipping a coin 3 times and getting at least 1 tail.
1 - probability of all heads: 1 - (1/2)^3 = 1 -1/8 = 7/8
A jar contains 10 marbles: 4 red, 3 blue, 3 green. Pick 2 marbles without replacement. Probability both are red?
P(First red): 4/10, P(second red:) 3/9 -> 4/10 x 3/9 = 12/90 = 2/15