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Roll two fair dice. Each die has six faces. A. Let A be the event that either a 3 or 4 is rolled first followed by an odd number. P(A) = .33 Round your answer to two decimal places. B. Let B be the event that the sum of the two dice is at most 7. P(B) = Round your answer to two decimal places. C. Are A and B mutually exclusive events? (Yes or No) yes D. Are A and B independent or dependent events? (Independent or Dependent)

Respuesta :

rodolforodriguezr

Answer:

A. 0.16

B. 0.58

C. No

D. Dependent

Step-by-step explanation:

A.

The sampling space has 36 outcomes.

The event A has 6 outcomes (3,1), (3,3), (3,5), (4,1), (4,3),(4,5)

So P(A)= 6/36 = 0.16

B.

The table in the picture shows the 15 outcomes that are not allowed, so there are 36-15 = 21 possible outcomes for B and its probability is 21/36 = 0.58

C.

Are A and B mutually exclusive events?

No since their intersection is not empty, for example (3,1) belongs to both A and B

D.

In order for A and B to be independent, it must happen that

P(A∩B)=P(A)P(B)

A∩B={(3,1),(3,3),(4,1)} so P(A∩B) = 3/36  

whereas

P(A)P(B) = (6/36)(21/36) = (1/6)(7/12)=7/72

So A and B are not independent.

Ver imagen rodolforodriguezr
mickymike92

Based on the total sample space, the probabilitiesare as follows:

  • Probabilityof A, P(A) = 0.16
  • Probability of B, P(B) = 0.58
  • A and B are not mutually exclusive events because their intersection is not empty
  • A and B are dependent events.

What is probability?

Probability refers to the likelihood or chance for a given event to occur or not.

  • Probability = number of expected outcomes/number of possible outcomes

For the given event where two fair die are rolled:

The sampling space has 36 outcomes.

Event A has 6 possible outcomes: (3,1), (3,3), (3,5), (4,1), (4,3),(4,5)

Probabilityof A, P(A) = 6/36

P(A) = 0.16

Event B has 21 possible outcomes

Probability of B, P(B) = 21/36

P(B) = 0.58

Mutually exclusive events are events which can not occur at the same time.

The intersection of mutually exclusive events is zero.(3,1) belongs to both A and B

Therefore, A and B are not mutually exclusive events because their intersection is not empty

For A and B to be independent;

  • P(A∩B)=P(A)P(B)

A∩B={(3,1),(3,3),(4,1)}

P(A∩B) = 3/36

However,

P(A)P(B) = (6/36) × (21/36)

P(A)P(B) = (1/6)(7/12)

P(A)P(B) =7/72

Since P(A∩B) is not equal to P(A)P(B), A and B are dependent events not independent.

Learn more about probability at: https://brainly.com/question/25870256

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