Probability is a measure of how likely an event is to occur. For example – Today there is a 60% chance of rain. The odds of winning the lottery are a million to one. What are some examples you can think of?
P ROBABILITY Probabilities are written as: Fractions from 0 to 1 Decimals from 0 to 1 Percents from 0% to 100%
P ROBABILITY If an event is certain to happen, then the probability of the event is 1 or 100%. If an event will NEVER happen, then the probability of the event is 0 or 0%. If an event is just as likely to happen as to not happen, then the probability of the event is ½, 0.5 or 50%.
P ROBABILITY Impossible Unlikely Equal Chances Likely Certain 0 0.5 1 0% 50% 100% ½
V OCABULARY Probability (P) – is the likelihood that an event will occur. Outcomes – when you do a probability experiment the different possible results are called outcomes Event – is a collection of outcomes
T YPES OF P ROBABILITY There are 2 types of probability Theoretical Probability Experimental Probability Let ’ s look at each one individually…
T HEORETICAL P ROBABILITY Theoretical Probability is based upon the number of favorable outcomes divided by the total number of outcomes Example: In the roll of a die, the probability of getting an even number is 3/6 or ½.
H OW DOES THAT WORK ? Each die contains the numbers 1, 2, 3, 4, 5, and 6. Of those numbers only 2, 4, and 6 are even. So, we can set up a ratio of the number of favourable outcomes divided by the total number of outcomes, which is 3/6 or 1/2
When a meteorologist states that the chance of rain is 50%, the meteorologist is saying that it is equally likely to rain or not to rain. If the chance of rain rises to 80%, it is more likely to rain. If the chance drops to 20%, then it may rain, but it probably will not rain. P ROBABILITY
What are some events that will never happen and have a probability of 0%? What are some events that are certain to happen and have a probability of 100%? What are some events that have equal chances of happening and have a probability of 50%?
P ROBABILITY The probability of an event is written: P(event) = number of ways event can occur total number of outcomes
P ROBABILITY P(event) = number of ways event can occur total number of outcomes An outcome is a possible result of a probability experiment When rolling a number cube, the possible outcomes are 1, 2, 3, 4, 5, and 6
P ROBABILITY P(event) = number of ways event can occur total number of outcomes An event is a specific result of a probability experiment When rolling a number cube, the event of rolling an even number is 3 (you could roll a 2, 4 or 6).
P ROBABILITY P(event) = number of ways event can occur total number of outcomes What is the probability of getting heads when flipping a coin? P(heads) = number of ways = 1 head on a coin = 1 total outcomes = 2 sides to a coin = 2 P(heads)= ½ = 0.5 = 50%
E XAMPLE # 1 A box contains 5 green pens, 3 blue pens, 8 black pens and 4 red pens. A pen is picked at random What is the probability that the pen is green? There are 5 + 3 + 8 + 4 or 20 pens in the box P (green) = # green pens = 5 = 1 Total # of pens 20 4
1. What is the probability that the spinner will stop on part A? 2.What is the probability that the spinner will stop on (a)An even number? (b)An odd number? 3. What is the probability that the spinner will stop in the area marked A? AB CD 31 2 A CB T RY T HESE :
P ROBABILITY W ORD P ROBLEM : Lawrence is the captain of his track team. The team is deciding on a color and all eight members wrote their choice down on equal size cards. If Lawrence picks one card at random, what is the probability that he will pick blue? Number of blues = 3 Total cards = 8 yellow red blue green black 3/8 or 0.375 or 37.5%
Donald is rolling a number cube labeled 1 to 6. What is the probability of the following? a.) an odd number odd numbers – 1, 3, 5 total numbers – 1, 2, 3, 4, 5, 6 b.) a number greater than 5 numbers greater – 6 total numbers – 1, 2, 3, 4, 5, 6 L ET ’ S W ORK T HESE T OGETHER 3/6 = ½ = 0.5 = 50% 1/6 = 0.166 = 16.6%
1. What is the probability of spinning a number greater than 1? 2.What is the probability that a spinner with five congruent sections numbered 1-5 will stop on an even number? 3. What is the probability of rolling a multiple of 2 with one toss of a number cube? T RY T HESE : 21 34
E XPERIMENTAL P ROBABILITY As the name suggests, Experimental Probability is based upon repetitions of an actual experiment. Example: If you toss a coin 10 times and record that the number of times the result was 8 heads, then the experimental probability was 8/10 or 4/5
E XPERIMENTAL P ROBABILITY F ORMULA Experimental Probability: P= Number of favorable outcomes Total number trials
E XAMPLE #2 In an experiment a coin is tossed 15 times. The recorded outcomes were: 6 heads and 9 tails. What was the experimental probability of the coin being heads? P (heads) = # Heads = 6 Total # Tosses 15
Another way to describe the chance of an event occurring is with odds. The odds in favor of an event is the ratio that compares the number of ways the event can occur to the number of ways the event cannot occur. We can determine odds using the following ratios: Odds in Favor = number of successes number of failures Odds against = number of failures number of successes
E XAMPLE #3 Suppose we play a game with 2 number cubes. If the sum of the numbers rolled is 6 or less – you win! If the sum of the numbers rolled is not 6 or less – you lose In this situation we can express odds as follows: Odds in favor =numbers rolled is 6 or less numbers rolled is not 6 or less Odds against = numbers rolled is not 6 or less `numbers rolled is 6 or less
E XAMPLE #4 A bag contains 5 yellow marbles, 3 white marbles, and 1 black marble. What are the odds drawing a white marble from the bag? Odds in favor = number of white marbles3 number of non-white marbles6 Odds against = number of non-white marbles6 number of white marbles3 Therefore, the odds for are 1:2 and the odds against are 2:1
Y OUR T URN - O DDS Find the favorable odds of choosing the indicated letter from a bag that contains the letters in the name of the given state. 5. S; Mississippi 6. N; Pennsylvania 7. A; Nebraska 8. G; Virginia
Y OUR T URN You toss a six-sided number cube 20 times. For twelve of the tosses the number tossed was 3 or more. 9. What is the experimental probability that the number tossed was 3 or more? 10. What are the odds in favour that the number tossed was 3 or more?
Y OUR T URN S OLUTIONS 5. 4/11 6. ¼ 7. ¼ 8. 1/8 9. 3/5 10. 3/2