Question

The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 4". Let B be the event "the outcome is greater than or equal to 4". Find P(A and B). Outcome Probability h 1 0.02 2 0.04 3 0.01 4 0.27 5 0.18 6 0.44 7 0.04

Answer 1

Probabilities

We are given a set of outcomes and their probabilities as follows:

x = {1 , 2 , 3 , 4 , 5 , 6 , 7}

P(x) = {0.02 , 0.04 , 0.01, 0.27 , 0.18 , 0.44 , 0.04}

Let A be the event "The outcome is less than 4"

Let B be the event "The outcome is greater than or equal to 4"

The elements of A are:

A = {1 , 2 , 3}

The elements of B are:

B = { 4 , 5 , 6 , 7}

The event (A and B) consists of all elements that are in A AND in B. We can see there are no elements in common in A and B, thus

P(A and B) = 0