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Probability for Dependent Events

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Wize University Statistics Textbook > Probability

Probability of Dependent Events (Conditional Probability)

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Given that P(A) = 0.6, P(B) = 0.5, and P(Bc|Ac)= 0.8, create a contingency table to answer the following questions.


More Probability of Dependent Events (Conditional Probability) Questions:
Conditional Probability
A certain pregnancy test is 98% effective in detecting an actual pregnancy. However, the test gives a "false positive" result for 2% of the non-pregnant women tested (i.e. if a woman is not pregenent and tries the test, the probability that the test will indicate pregnancy is 0.02). If 20% of women in a particular group are in fact pregnant, what is the probability that a women selected at random from this group is pregnant if the result is positive?
Conditional Probability
A blue and red die are tossed at the same time. If it’s known that the sum of the two dice is 99, what is the probability that the blue die shows a 44?
Two-Way Table Practice Question
40% of children eat strawberries. Of those that eat strawberries, 80% are vegetarian. Half of those that don’t eat strawberries are vegetarian.
Bernoulli Trials & Conditional Probability
Four teams are competing in a hot dog eating contest where they must finish eating 20 hot dogs in the given amount of time. For each team, the probability of them finishing the contest is 0.6 If at least one team finished the contest, determine the probability that all Four of them did.
Probability of Dependent Events (Conditional probability)
This table shows whether passengers on a flight to New York like to fly and/or like to drive.
Let F be the event that a randomly selected passenger likes to fly.
Let D be the event that a randomly selected passenger likes to drive.
Probability of Dependent Events (Conditional Probability)
An on-campus survey asked 200 students where their home town is, and here is the frequency distribution of their answers.
Home TownCalgaryTorontoMontrealVancouverFrequency80751530\begin{array}{|c|c|c|c|c|} \hline \text{Home Town}&\text{Calgary}&\text{Toronto}&\text{Montreal}&\text{Vancouver}\\ \hline \text{Frequency}&80&75&15&30\\ \hline \end{array}
If a randomly selected student told us that he/she is not from Toronto, what is the probability that he/she is from Calgary?
Conditional Probability
A certain pregnancy test is 98% effective in detecting an actual pregnancy. However, the test gives a "false positive" result for 2% of the non-pregnant women tested (i.e. if a woman is not pregenent and tries the test, the probability that the test will indicate pregnancy is 0.02). If 20% of women in a particular group are in fact pregnant, what is the probability that a women selected at random from this group is pregnant if the result is positive?
Probability of Dependent Events (Conditional Probability)
The probability that a first year student is enrolled in BMOS is 0.40. 30% of all BMOS students take calculus and 20% of students not in BMOS take calculus.
Probability for Dependent Events 2
Gloria is an opera singer. The probability that she will get a standing ovation is 60%. The probability that she will have a wardrobe malfunction is 20%. The probability that she will only get a standing ovation is 55%.
Bayes' Theorem: Conditional Probability
Katie could put a ball in either Slot A or Slot B and hopes to win a prize. The ball will bounce around and will either land in a winning box or the losing box. Suppose she puts the ball in Slot A 40% of the time; Slot B 60% of the time. If she puts the ball in Slot A, the ball lands in the winning box 15% of the time. If she puts the ball in Slot B, the ball lands in the losing box through the first channel 60% of the time and into the same losing box through the second channel 20% of the time. See illustration below:
Katie won. What is the probability that she put the ball in Slot A?
Probability of Dependent Events
Half of students own an Apple product. One-quarter of all students wear glasses. 35% of all students do not wear glasses and nor own Apple products.
Use the contingency table from the previous question to answer the following questions below. [Click on Hint to see the full contingency table.]
Probability of dependent events: Conditional probability
Mizter Chi raps about statistics: 30% about descriptive statistics and 70% about inferential statistics. Based on his songs, 62% of them contains profanity, but 80% of his songs about inferential statistics contains profanity. What percentage of his songs about descriptive statistics does not contain profanity?
Probability of Dependent Events: Conditional Probability
Let A and B be two events where P (A) = 0.7 and P (B) = 0.5. Which of the following is false?