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Applications of Mathematics 12
theoretical probability
name: _________________
Theoretical Probability
date: ________________
Theoretical Probability is a probability prediction determined using the ratio:
Probability of an event = P(E) =
The more trials that an experimental probability has, the closer it comes to the theoretical probability.
Yesterday’s simulations:
Given the toss of a coin 100 times the P(H) =
Given the toss of a coin ________ times the P(H) =
The theoretical probability of the coin landing head up
P(H) =
Given the roll of a six sided fair dice, 100 rolls, the P(5) =
Given the roll of a six sided fair dice, _________rolls, the P(5) =
The theoretical probability of the dice landing 5 up
P(5) =
What does a deck of standard playing cards look like ?
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Applications of Mathematics 12
theoretical probability
EXAMPLE 1:
What is the theoretical probability of picking
a black queen from a regular 52 card pack?
EXAMPLE 2:
What is the theoretical probability of getting
a red light if a traffic light shows red for 110 seconds,
yellow for 10 seconds and green for 180 seconds?
EXAMPLE 3:
In the game of “In Between” 3 cards are dealt from a standard 52 card pack. To win, the third card has
to be in between the first two. What is the theoretical probability of winning if the first two cards dealt
are:
(a)
3 and 9?
(b)
jack and queen?
EXAMPLE 4:
Tyler draws a card from a regular deck of playing cards and it is red. He does 10 such trials, replacing
the card each time. out of the ten times, a red card appears 7 times. He makes the statement
“The theoretical probability of drawing a red card is 0.7”
(a)
Why is his statement incorrect?
(b)
What could Tyler do to enable the experiment to arrive closer to the theoretical probability?
(c)
What is the theoretical probability of drawing a red card from a regular deck of playing cards?
(d)
Can Tyler’s experiment be called a binomial experiment? Why/ why not ?
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ASSIGNMENT:
name: ______________
Give all answers as fractions in lowest terms.
1.
2.
3.
An 8-sided die is rolled. The faces are numbers from 1 to 8.
(a)
What is the theoretical probability of getting a 5?
(b)
What is the theoretical probability of getting an odd number?
A 12-sided die is rolled. The faces are numbered from 1 to 12.
(a)
What is the theoretical probability of getting a 7?
(b)
What is the theoretical probability of getting an even number?
One card is drawn from a standard deck of 52 playing cards. Determine the following theoretical
probabilities.
(a)
The card is a black king.
(b)
The card is even numbered and red.
** Face cards do not count as numbered cards.
(c)
4.
The card is a red ace.
One card is drawn from a deck of face cards, a deck which contains only the jack, queen, and king
of each of the four suits. Determine the following theoretical probabilities.
(a)
The card is a red queen.
(b)
The card is a king.
(c)
The card is a male face card.
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5.
6.
7.
A regular 6-sided die is rolled 50 times. The number 6 appears 10 times.
(a)
What is the experimental probability of a 6?
(b)
What is the theoretical probability of a 6?
A 5-sided die numbered 1 to 5 is tossed 120 times. The die lands on an even number 50 times.
(a)
What is the experimental probability of an even number?
(b)
What is the theoretical probability of an even number?
In a raffle, 300 tickets are sold. Determine the theoretical probability of winning if you purchase:
(a)
8.
1 ticket
(b)
20 tickets
A roulette wheel consists of 40 numbers: 1 to 38, 0 and 00. The odd numbers are coloured black,
the even numbers are coloured red, and the numbers 0 and 00 are coloured green. Determine the
following theoretical probabilities.
(a)
The ball will come to rest on a red coloured number.
(b)
The ball will come to rest on the number 7.
(c)
The ball will come to rest on a green coloured number.
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