General Probability (Practice Problems)

Question 1

Suppose that 7% of people in town have cancer. Suppose a test can determine if a patient is positive for cancer for 89% of patients with cancer but is also 5% positive for those without cancer. If selected at random what is the probability a person has cancer given a positive test result?

Answer 1

P(positive)=.1088
P(Cancer/Positive)= P(Cancer and Positive)/ P(Positive)
Answer = .573 or 57.3%

Question 2

If a player rolls two dice and gets a sum of 2 or 12 he wins $20. If the person gets a 7 he wins $5. The cost to play the game is $3. Find the expectation of the game.

Answer 2

Expectation=the mean

E(x)= 1.165

Question 3

Probability of getting accepted to Yale is 0.7 and the probability of being accepted to Princeton is 0.6. Probability of getting accepted to both is 0.4. a) Probability of getting accepted to one school? b) Not accepted to either school?

Answer 3

a) 0.9

b) 0.1

Question 4

Suppose a chocolate company has three factories. 40% of their chocolate is made at factory 1 and 80% is dark chocolate 25% of chocolate is made at factory 2 and 30% is milk chocolate. Rest of the chocolate is made in Factory 3 and 65% is dark chocolate. a)Probability of milk chocolate? b) if you have dark chocolate what the probability it came from factory 2?

Answer 4

a) P(milk chocolate)= 0.2775

b) P(dark/2)= .2422

Question 5

Central is playing Centennial. If Central’s 1st quarterback plays they have a 75% of winning. if they play the backup QB their chances drop to 40%. The chance of the 1 QB playing is 70%. a) Probability of winning the game? b) If central won was was the probability the backup QB played?

Answer 5

a) P(winning)= .645

b) P(Backup QB/ Winning)= .186