Question

1. Suppose we have a six-sided die that we roll once. Let ai represent the event that the result is i. Let Bj represent the event that the dice comes out greater than j. Let C represent the event that the result is an even number.

a) Since the number is greater than 1, what is the conditional probability that 3 is obtained? (P[A3|B1])

b) Since the number is greater than 3, what is the conditional probability that 6 is obtained?

c) Since the result is an even number, what is the conditional probability of a number greater than 3? (ie P[B3|C])

d) Since the number is greater than 3, what is the conditional probability of an even number?

Answer 1

Using the probability concept, it is found that there is a

a) 0.2 = 20% probability that 3 is obtained.

b) 0.3333 = 33.33% probability that 6 is obtained.

c) 0.6667 = 66.67% probability of a number greater than 3.

d) 0.6667 = 66.67% probability of an even number.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item a:

There are 5 numbers greater than 1, one of which is 3, hence:

$p = \frac{1}{5} = 0.2$

0.2 = 20% probability that 3 is obtained.

Item b:

There are 3 numbers greater than 3, one of which is 6, hence:

$p = \frac{1}{3} = 0.3333$

0.3333 = 33.33% probability that 6 is obtained.

Item c:

There are 3 even numbers, two of which are greater than 3, hence:

$p = \frac{2}{3} = 0.6667$

0.6667 = 66.67% probability of a number greater than 3.

Item d:

There are 3 numbers greater than 3, two of which are even, hence:

$p = \frac{2}{3} = 0.6667$

0.6667 = 66.67% probability of an even number.

A similar problem is given at https://brainly.com/question/25667645