Question

Question 7 (1 point) Use following diagram to answer the question 9 Given that right die shows an even number, what is the probability that left die shows a multiple of 3 2/3 1/3 o RI w е oo hu

Answer 1

Answer

We want to Find given that right die shows an even number, what is the probability that left die shows a multiple of 3?

That is,

P(left die shows a multiple of 3/Right die shows an even number)

We are given that,

Number of total sample space = n(S) = 24

Here consider an events,

A= Left die shows a multiple of 3

B= Right die shows an even number

Therefore,

P(A/B) = P(A and B)/ P(B)

Here,

(A and B) = {(3,4),(3,6),(6,4),(6,6)}

So, n(A and B) =4

n(S) = 24

P(A and B) = n(A and B ) / n(s) = 4/24

(B) = {(1,4),(1,6),(2,4),(2,6),(3,4),(3,6),(4,4),(4,6),(5,4),(5,6),(6,4),(6,6)}

n(B) = 12

n(S) = 24

P(B) = n(B)/n(S) = 12/24

Since,

P(A/B)

= P( A and B)/P(B)

= (4/24)/(12/24)

= 1/3

Therefore,

The probability that left die shows a multiple of 3 given that right die shows an even number is,

1/3.