probabilities of simple events.pptx

PowerPoint Presentation

Probability

Vocabulary:

Outcome one possible result of a probability.Sample Space the list of possible outcomes for a probability event.Random outcomes that occur at random if each outcome is equally likely to occur.Simple Event a specific outcome or type of outcome. Complementary Events the events of one outcome happening and that outcomes not happening are complimentary; the sum of the probabilities of complementary events is 1.What is a PROBABILITY?

- Probability is the chance that some event will happen

- It is the ratio of the number of ways a certain event can occur to the number of possible outcomesProbability of Simple EventsProbabilityProbability 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?

What is a PROBABILITY?

number of favorable outcomes number of possible outcomes

Examples that use Probability:(1) Dice, (2) Coins, (3) Deck of Cards, (4) Evens/Odds, (5) Alphabet, etc.Probability of Simple EventsP(event) = What is a PROBABILITY?

0% 25% 50% 75% 100%

0 or .25 0r .5 or .75 1

Impossible Not Very Equally Likely Somewhat Certain Likely LikelyProbability of Simple EventsProbabilityProbabilities are written as:

Fractions from 0 to 1

Decimals from 0 to 1

Percents from 0% to 100%

ProbabilityIf 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 , 0.5 or 50%.

ProbabilityImpossible Unlikely Equal Chances Likely Certain 0 0.5 1 0% 50% 100% 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.

ProbabilityProbabilityWhat 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%?

ProbabilityThe probability of an event is written:

P(event) = number of ways event can occur total number of outcomes

ProbabilityP(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


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).


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)= = 0.5 = 50%

Example 1: Roll a dice.What is the probability of rolling a 4?

# favorable outcomes # possible outcomes

1 6

The probability of rolling a 4 is 1 out of 6Probability of Simple EventsP(event) = P(rolling a 4) =

Example 2: Roll a dice.What is the probability of rolling an even number?


3 1 6 2

The probability of rolling an even number is 3 out of 6 or .5 or 50%Probability of Simple EventsP(event) = P(even #) = =Example 3: Spinners.What is the probability of spinning green?


1 1 4 4

The probability of spinning green is 1 out of 4 or .25 or 25%Probability of Simple Events

P(event) = P(green) = =Example 4: Flip a coin.What is the probability of flipping a tail?


1 1 2 2

The probability of spinning green is 1 out of 2 or .5 or 50%Probability of Simple Events

P(event) = P(tail) = =Example 5: Deck of Cards.What is the probability of picking a heart?

# favorable outcomes 13 1

# possible outcomes 52 4The probability of picking a heart is1 out of 4 or .25 or 25%What is the probability of picking a non heart?

# favorable outcomes 39 3

# possible outcomes 52 4The probability of picking a heart is3 out of 4 or .75 or 75%

Probability of Simple EventsP(heart) = = =

P(nonheart) = = =Key Concepts:

- Probability is the chance that some event will happen

- It is the ratio of the number of ways a certain even can occur to the total number of possible outcomesProbability of Simple EventsGuided Practice: Calculate the probability of each independent event.

1) P(black) = 2) P(1) = 3) P(odd) = Probability of Simple Events

Guided Practice: Answers.

1) P(black) = 4/82) P(1) = 1/83) P(odd) = 1/2Probability of Simple Events

Independent Practice: Calculate the probability of each independent event.

1) P(red) = 2) P(2) = 3) P(not red) = 4) P(even) = Probability of Simple Events

Independent Practice: Answers.

1) P(red) = 1/22) P(2) = 1/43) P(not red) = 1/24) P(even) = 1/2Probability of Simple Events

Real World Example:A computer company manufactures 2,500 computers each day. An average of 100 of these computers are returned with defects. What is the probability that the computer you purchased is not defective?

P(not defective) = # not defective= 2,400 = 24 total # manufactured 2,500 25Probability of Simple Events1. What is the probability that the spinner will stop on part A?What is the probability that the spinner will stop on An even number?An odd number?3. What is the probability that the spinner will stop in the area marked A?ABCD312ACBTry These:Probability Word Problem: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 = 3Total cards = 8

yellowredbluebluebluegreenblackblack3/8 or 0.375 or 37.5%Lets Work These TogetherDonald 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, 63/6 = = 0.5 = 50%1/6 = 0.166 = 16.6%

probabilities of simple events.pptx

Documents