Question

1. Event A occurs with a likelihood of .45. Event B occurs with a likelihood of .35. If Event B occurs, then Event

A cannot have occurred. What is the likelihood of either Event A or Event B occurring?

2. Alice flips two fair coins, and rolls a single 20-sided die. What is the probability that she will get exactly one heads (out of two) and a die roll that is divisible by 5?

3. Using probabilistic terms, how would you describe the events described in the previous two questions?

Answer 1

(a)

Given:
P(A) =0.45

P(B) = 0.35

Events A and B are mutually exclusive.

By Addition Theorem of Probability of Mutually Exclusive Events, we get:
P(A + B) = P(A) + P(B)

          = 0.45 + 0.35

         = 0.80

So, Answer is:

0.80

(b)

Let

A = getting exactly 1 Head in 2 coins

B = getting a number of divisible by 5 of 20 sided die

To find P(A) = P(getting exactly 1 Head in 2 coins):

Number of events:

{HH,HT,TH,TT}: 4 Nos.

Favorable events:

{HT,TH}: 2 Nos.

So,

P(A) = P(getting exactly 1 Head in 2 coins):= 2/4 = 0.50

To find P(B)= P( getting a number of divisible by 5 of 20 sided die)

Number of events = 20

Favorable events:

{0,5,10,15,20}: 5 Nos.

So,

P(B)= P( getting a number of divisible by 5 of 20 sided die) = 5/20 = 0.25

By Multiplication Theorem of Probability of Independent Events, we get:
P(AB) = P(A) X P(B)

          = 0.50 X0.25

         = 0.125

So, Answer is:

0.125

(c)

Using probability terms, we would describe the events in (a) as Mutually Exclusive Events.

Using probability terms, we would describe the events in (b) as Independent Events.