Page 33 - Insurance Times April 2023

occurring in the presence of a second event. Divide the number of ways to achieve the desired
outcome by the number of total possible outcomes to
p (A|B) is the probability of event A occurring, given that
calculate the weighted probability. To finish the example,
event B occurs. Example: given that you drew a red card,
you would divide five by 36 to find the probability to be
what's the probability that it's a four (p(four|red))=2/
0.1389, or 13.89 percent.
26=1/13. So out of the 26 red cards (given a red card),
there are two fours so 2/26 = 1/13. Game probability:
Axiomatic Probability: The probability of rolling a 6 is 1/6 (there are six numbers,
so you roll a six one time out of every 6) The probability
It is a type of probability that has a set of axioms (rules)
of not rolling a six is 5/6 (rolling any of the other five
attached to it and a rule that the probability must be
numbers)
greater than 0%, that one event must happen, and that
one event cannot happen if another event happens. Playing card probability:
Let's look at one probability in these two ways:
Weighted probabilities:
Probabilities represent the chances that different events What is the probability of drawing a card from a deck
will occur. For example, if you were rolling a single six- and it being red and a face card?
sided die, you would have the same probability of rolling
For this probability, we need to look at which cards are
a one as rolling any other number because each number
both red and face cards. There are 6 of these: Jack of
will come up one out of six times. However, not all
Hearts, Queen of Hearts, King of Hearts, Jack of
scenarios have each outcome equally weighted. For
Diamonds, Queen of Diamonds, and King of Diamonds.
example, if you add a second die to the mix, the odds of
P= 6/52 = 3/26 = 11.5%
the dice adding up to two are significantly less than
adding up to seven. This is because there is only one die OR
combination (1,1) that results in two, while there are This time the card can be red, or a face card, or both at
numerous die combinations--such as (3,4), (4,3), (2,5) the same time. There are 26 red cards (6 of which are
and (5,2)--that results in seven. also face cards). In addition, there are 6 more face cards
Determine the total number of possible outcomes for that are not red: Jack of Clubs, Queen of Clubs, King of
Clubs, Jack of Spades, Queen of Spades, and King of
the scenario. For example, with rolling two dice, there
Spades. That is a total of 26 + 6 = 32 cards.
are 36 possible outcomes because there are six outcomes
for each die so you would multiply six times six. 32/52 = 8/13 = 61.5%
Determine how many ways the desired outcome can Be careful not to just add up the number of face cards (12)
occur. For example, if you are playing a board game and with the number of red cards (26). That would give a total of
will win if you roll an eight, you would need to determine 38 cards, but it would count the red face cards twice.
how many ways an eight could be rolled, which is five:
(2,6), (3,5), (4,4), (5,3) and (6,2).

The Insurance Times April 2023 29