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Use for Questions 1-7: Hector will roll two fair, six-sided dice at the same time. Let...

Use for Questions 1-7: Hector will roll two fair, six-sided dice at the same time. Let A = the event that at least one die lands with the number 3 facing up. Let B = the event that the sum of the two dice is less than 5.

1. What is the correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5”?

2. Calculate the probability that at least one die lands with 3 facing up and the sum of the two dice is less than 5.

3. What is the correct set notation for the event that “at least one die lands with 3 facing up if the sum of the two dice is less than 5”?

4. Calculate the probability that at least one die lands with 3 facing up if the sum of the two dice is less than 5.

5. What is the correct set notation for the event that “the sum of the two dice is not less than 5 if at least one die lands with 3 facing up”?

6. Calculate the probability that the sum of the two dice is not less than 5 if at least one die lands with 3 facing up.

7. Are A and B independent? Explain your reasoning

Solutions

Expert Solution

From the given problem we observe that when two dice are thrown A be the event that atleast one die lands with the number 3 facing up

B be the event that sum of the two dice is less than 5

1.outcomes of the event atleast one die lands with 3 facing up are (1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6) and sum of two dice is less than 5 are (1,2),(1,3),(2,1)(2,2),(3,1) he outcomes of(A and B) are (3,1), (1,3)

2.probability that atleast one die lands with 3 facing up and sum of two dice less than 5 is given as

P(A and B)= n(A and B) /N= 2/36 =1/18 where N= 62=36

3.outcomes of the event A are (1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6)

outcomes of the event B are (1,2),(1,3),(2,1)(2,2),(3,1)

the outcomes of the event A given B are (1,3),(3,1) of (1,2),(1,3),(2,1)(2,2),(3,1)

4. proabability of A given B is given as P(A/B) = P(A and B) /P(B) =(2/36)/(5/36)=2/5

5 outcomes of the .event that the sum of two dice is not less than 5 if atleast one die lands with 3 facing up are (3,2),(3,3),(3,4),(3,5),(3,6),,(2,3),(4,3),(5,3),(6,3)

6.Probability that the sum is not less than 5 if the atlest one die lands with 3 facing up = 9/11

here 11= no.of outcomes of atleast one die lands with 3 facing up

7. A and B are not independent since happening of the event A is influenced by happening of the event B   

  

milcah answered 2 hours ago
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