Презентация Conditional probability and the multiplication rule онлайн
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Слайды и текст к этой презентации:
№1 слайд
Содержание слайда: Conditional Probability and the Multiplication Rule
Unit 3.3
№2 слайд
Содержание слайда: Multiplication Rule
The Multiplication Rule can be used to find the probability of two or more events that occur in a sequence .
The multiplication Rule for the probability of A and B
If events A and B are independent, then the rule can be simplified to P(A and B) = P (A) ● P (B). This simplified rule can be extended for any number of independent events.
№3 слайд
Содержание слайда: Multiplication Rule Tip
Find the probability the first event occurs.
Find the probability the second event occurs given the first event has occurred and
Multiply these two probabilities.
№4 слайд
Содержание слайда: Using the Multiplication Rule to find Probability
A coin is tossed and a die is rolled. Find the probability of getting a head and then rolling a 6.
№5 слайд
Содержание слайда: Using the Multiplication Rule to find Probability
A card is drawn from a deck and replaced; then a second card is drawn. Find the probability of selecting a Ace and then selecting a queen.
№6 слайд
Содержание слайда: Using the Multiplication Rule to find Probability
The probability that a salmon swims successfully through a dam is 0.85. Find the probability that two salmon successfully swim through the dam.
№7 слайд
Содержание слайда: Using the Multiplication Rule to find Probability
Two cards are selected from a standard deck without replacement. Find the probability that both are hearts.
№8 слайд
Содержание слайда: Using the Multiplication Rule to find Probability
A Harris poll found the 46% of Americans say they suffer great stress at least once a week. If three people are selected at random, find the probability that all three will say they suffer great stress at least once a week.
№9 слайд
Содержание слайда: Using the Multiplication Rule to find Probability
The probability that a salmon swims successfully through a dam is 0.85. Find the probability that three salmon swim successfully through the dam.
№10 слайд
Содержание слайда: Using the Multiplication Rule to find Probability
Find the probability that none of the three salmon are successful.
№11 слайд
Содержание слайда: Using the Multiplication Rule to find Probability
Find the probability that at least one of the three salmon is successful in swimming through the dam.
№12 слайд
Содержание слайда: Dependent Events
When the outcome or occurrence of the first event affects the outcome or occurrence of the second event in such a way that the probability is changed, the events are said to be dependent events.
Examples
Drawing a card from a deck, NOT replacing it, and then drawing a second card.
Being a lifeguard and getting a tan.
Having high grades and getting a scholarship
№13 слайд
Содержание слайда: Conditional Probability
To find probabilities when events are dependent, use the multiplication rule with a modification in notation.
P(A and B) = P (A) ● P (B\A).
№14 слайд
Содержание слайда: Finding Conditional Probability
Two cards are selected in sequence from a standard deck. Find the probability that the second card is a queen, given that the first card is a king. (Assume that the king is not replaced)
Solution: Because the first card is a king and is not replaced, the remaining deck has 51 cards, 4 of which are queens. So,
P(B|A) = 4/51 = 0.078
№15 слайд
Содержание слайда: Finding Conditional Probability
Three cards are drawn from an ordinary deck and not replaced. Find the probability of these events.
Getting 3 Jacks
Getting an ace, a king, and a queen in order
Getting a club, a spade, and a heart in order
Getting three clubs
№16 слайд
Содержание слайда: Finding Conditional Probability
The table at the left shows the results of a study in which researchers examined a child’s IQ and the presence of a specific gene in the child. Find the probability that a child has a high IQ given that the child has the gene.
Solution: There are 72 children who have the gene. So, the sample space consists of these 72 children, as shown at the left. Of theses, 33 have a high IQ. So,
P(B\A)= 33/72 =0.458
№17 слайд
Содержание слайда: Finding Conditional Probability
Find the probability that a child does not have the gene.
Find the probability that a child does not have the gene, given that the child has a normal IQ.
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