1. WHAT ARE MY CHANCES? WHAT ARE THE PROBABILITIES?
Remember the formula for calculating probability:
Probability = Total number of favourable outcomes
Total number of equally possible outcomes
Calculate your probabilities in a card draw:
1. What is the possibility of drawing a Queen from a deck of cards?
(Hint: there are 4 different suits in a deck of cards - hearts, diamonds,
spades and clubs. Each suit has 13 cards, ranging from Ace or one to 10
and then a Jack, Queen and King. Therefore, there are 13 cards
in each of the 4 suits.) So, divide the total number of Queen cards
(Answer: 4) by the total number of cards in the deck (Answer: 52)
Answer: 4/52 or 1/13 (although not asked to calculate this, the
percentage is 7.7%).
If you have a deck of cards, draw one and note which card it was:
______________________________________________________________________________________________
Was it a Queen? Yes / No
2. What is the possibility of drawing a number lower than 9 from a deck of
cards?
(Hint: there are 4 suits with numbers 1-10, Jack, Queen and King in each.
In this case, an Ace counts as 1) (Answer: each suit has 8 cards lower than
9, i.e. numbers 8,7,6,5,4,3,2,and Ace. There are 4 suits, therefore the
total number of cards less than 9 are 8x4 = 32. Divide by the total number
of cards = 52.
Answer: 32/52 or 8/13 (although not asked to calculate this, the
percentage is 61.5%)
If you have a deck of cards, draw one and note which card it was:
___________________________________________________________________________________________
Was it a lower than 9? Yes / No
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Unit 8.3
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2. Calculate the probabilities in a Lotto draw:
3. In a Lotto game you choose 6 numbers from 1-49. The total number of
combinations of winning the 1st prize (of getting all 6 numbers) is :49 x
49 x 49 x 49 x 49 x 49 (or 496
). The probability of winning first prize is
1 in 14 million! Therefore, there a good chance you could win 1st prize.
True or false? (Answer: False!)
4. In a Lotto draw, you stand a better chance (i.e. a higher probability) of
winning if you:
a) chose numbers that have not been in the previous week's winning
numbers. (Answer: False)
b) just choosing the numbers 1,2,3,4,5,6 every time?
True or false?
(Answer: False. The process of selecting the numbers in a Lotto draw is
totally random. That means there is no pattern, no connection between the
numbers chosen or between the previous weeks' draws and the current
one. Each of the 49 numbers has an equal chance of being drawn for each
of the 6 slots. You therefore stand the same chance of winning if you chose
1,2,3,4,5,6 every week or 13,1,8,27,33,46 every week, or some
combination based on birthdays, or any other combination of six
numbers.)
Calculate the probability in everyday occurrences:
5. Eighteen athletes with numbers 1 to 18 are running in the school race. The
probability that the athlete numbered 7 will win is 1/18. True or false?
(Answer: False. Running a race is not a random event. It is determined
largely by skill and training. Of course, luck, as in all matters of life, can
also play a part, for example if the fastest runner happens to be suffering
from a bad cold that day.)
6. A couple has 3 daughters. If they have another baby it is likely to be a boy
because 4-girl families are uncommon. True or false?
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3. Answer: False. It is true that 4-girl families are uncommon, but in
general having had a boy or girl previously has no influence on the gender
of the next child, i.e., we assume that births are independent events.
Actually, this isn't entirely accurate. The true probability is not exactly
50/50 due to rates of conception, miscarriages, and other environmental
and physiological factors. A boy is more likely to be born (with a
probability of 51.21%) than a girl (with a probability of 48.79%).
7. There are 26 letters in the English alphabet. If I select a letter at random
from the page of an English novel, the probability that it will be an “e” is
1/26. True or false?
Answer: False. As any Scrabble player knows, there are some letters (like
vowels) that appear much more often than other letters (like x or y).
8. Elizabeth doesn't know the answer to a 4-answer multiple choice question.
She is going to guess a, b, c or d. The probability that she will guess
incorrectly is 3/4. True or false?
Answer: True.
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