Problem14: Probability

¡Puedes leer este texto en español! Problema14: Probabilidad

Ej14. For some dice, the probability of being a face, when pulled, is proportional to the number of points that it showed. Calculate the probability of getting with this dice, an even number.

The sample space of the dice is:

Ω = {1, 2, 3, 4, 5, 6}

The probability of getting any value of the dice is proportional to its value.

So, we have to get all values that there in a dice:

Total points = 1+2+3+4+5+6 = 21

To get an element, its probability will be its value among the total points of the dice, in other words:

P(1) = 1/21, P(2) = 2/21, P(3) = 3/21, P(4) = 4/21, P(5) = 5/21, P(6) = 6/21

It creates the following event:

A Ξ “It's an even number”

The event A has the following elements:

A = {2, 4, 6}

And finally, the probability of event A, is the sum of the probabilities of all its components:

P(A)= P(2) + P(4) + P(6) = 2/21 + 4/21 + 6/21 = 12/21 = 4/7