Respuesta :
First roll: 3/6
Second roll:2/6
Probability that the first roll is an even number AND the second roll is a number greater than Four is
(3/6)*(2/6) = 6/36 or 1/6 or approx 0.167 or 16.7%
Second roll:2/6
Probability that the first roll is an even number AND the second roll is a number greater than Four is
(3/6)*(2/6) = 6/36 or 1/6 or approx 0.167 or 16.7%
The probability that a first roll is an even number and a second role is a number greater than 4 when a six-sided number cube is rolled twice is 1/6.
What is the probability of an event?
The probability of an event is the fractional value determining how likely is that event to take place. If the event is denoted by A, the number of outcomes favoring the event A is n and the total number of outcomes is S, then the probability of the event A is given as:
P(A) = n/S.
What are independent events?
When the occurrence of one event, doesn't affect the occurrence of the other event, then the two events are independent of each other.
If we have two independent events A and B, then the probability of A and B is given as:
P(A and B) = P(A) * P(B).
How do we solve the given question?
We are informed that a six-sided number cube is rolled twice. We are asked what is the probability that a first roll is an even number and a second roll is a number greater than 4.
Let the event of getting an even number on a first roll be A.
∴Number of outcomes favorable to event A (n) = 3 {2, 4, 6}
Total number of outcomes (S) = 6 {1, 2, 3, 4, 5, 6}
∴ The probability of getting an even number on a first roll is:
P(A) = n/S = 3/6 = 1/2.
Let the event of getting a number greater than 4 on a second roll be B.
∴Number of outcomes favorable to event B (n) = 2 {5, 6}
Total number of outcomes (S) = 6 {1, 2, 3, 4, 5, 6}
∴ The probability of getting a number greater than 4 on a second roll is:
P(B) = n/S = 2/6 = 1/3.
∵ Our two events, A and B, are independent of each other, that is, the occurrence of one doesn't affect the occurrence of the other, the probability that a first roll is an even number and a second roll is a number greater than 4 is given by:
P(A and B) = P(A)*P(B) = (1/2)*(1/3) = 1/6.
∴ The probability that a first roll is an even number and a second role is a number greater than 4 when a six-sided number cube is rolled twice is 1/6.
Learn more about the probability of independent events at
https://brainly.com/question/7965468
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