A Collection of Probability
Questions
1. Determine the probability of each
of the following situations
a) A red card is drawn from a standard deck
There are 52 cards in a deck. Half of them
are red (26), so…
26
1

52
2
b) 2 even numbers are rolled on two consecutive rolls of a die.
Rolling an even number (3 even numbers, 6
numbers total), is 3/6 = ½
Rolling 2 even numbers in a row, would be
the product.
1
1 1


2 2
4
c) At least one three turns up when three dice are rolled.
Each roll has a 1/6 chance of occuring
At least 1 three could be 1, or 2, or 3 (three
cases)
The indirect method will be faster
The compliment of “at least 1 three”, is no threes
5 5 5 125
  
6 6 6 216
125
91
1

216 216
d) Dealing a hand from a standard deck. Three of one
suit and two of another.
13 cards per suit, you need 3 of them, so 13C3
There are 4 choices for suits, so 4 X 13C3
13 cards per suit, you need 2 of them, so 13C2
There are 3 choices for suits, so 3 X 13C2
13
13
4     3   
2
3


 
 52
 
5 
e) Two face cards are drawn in a row (without
replacement) from a standard deck given that the first
card drawn is a king.
First card drawn is a king.
The next draw is a face card (there are 11 face
cards left, and 51 cards left)
4 11
44
11
 

52 51 2652 663
f) A committee of six people randomly chosen from
seven males and eight females is either all male or all
female.
All male, 7C6
All female, 8C6
All committees, 15C6
 7  8 
    
6 6
15
 
6 
g) In a six person sprint, Jesse finishes first, Marnie
second, and Raul last.
Jesse first:1
Marnie second: 1
Raul last: 1
3 spots left for 3 people (3!)
6! Total ways
3!
6!
• See the sheet
outline posted