Page 203 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes Three of a kind is a hand, like 5557K, where three cards have the similar rank while the
remaining 2 vary in rank among themselves and the first three. There are 13 × C(4, 3) = 52 combinations
of three cards of the similar rank. The next card could be any of 48 and the fifth any of 44 and the pair
could come in any order so the products is required to be halved: 52 × 48 × 44 / 2 = 54912.

Example: A spinner has 4 equal sectors colored yellow, blue, green and red. After spinning
the spinner, what is the probability of landing on each color?

The possible conclusions of this experiment are yellow, blue, green, and red.
# of ways to land on yellow 1
P(yellow) = 
total # of colors 4
# of ways to land on blue 1
P(blue) = 
total # of colors 4

# of ways to land on green 1
P(green) = 
total # of colors 4
# of ways to land on red 1
P(red) = 
total # of colors 4

Example: A single 6-sided die is rolled. What is the probability of each conclusion? What
is the probability of rolling an even number? of rolling an odd number?
The possible conclusions of this experiment are 1, 2, 3, 4, 5 and 6.
Probabilities:
# of ways to roll a 1 1
P(1) = 
total # of sides 6

# of ways to roll a 2 1
P(2) = 
total # of sides 6
# of ways to roll a 3 1
P(3) = 
total # of sides 6
# of ways to roll a 4 1
P(4) = 
total # of sides 6
# of ways to roll a 5 1
P(5) = 
total # of sides 6

# of ways to roll a 6 1
P(6) = 
total # of sides 6
# ways to roll an even number 3 1
P(even) =  
total # of sides 6 2
# ways to roll an odd number 3 1
P(odd) =  
total # of sides 6 2
This example shows the difference between a conclusion and an event. A single conclusion of
this experiment is rolling a 1, or rolling a 2, or rolling a 3, etc. Rolling an even number (2, 4
or 6) is an event, and rolling an odd number (1, 3 or 5) is also an event.

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