Question

rdinary fair die is rolled. If the die shows an odd number then S, the score awarded, is equal to that
number. If the die shows an even number, then the die is rolled again. If on the second roll it shows an odd
number, then that is the score awarded. If the die shows an even number on the second roll, the score awarded
is equal to half of that even number.
a List the possible values of S and draw up a probability distribution tab

Answer 1

$Sample \space space,S=\{1,2,3,4,5,6\}\\$

Let A be the event of getting an odd number.

Let B be the event of getting a prime number.

$A=\{1,3,5\},B=\{2,3,5\},A∩B={3,5}$

The conditional probability of event B given that A has already occurred, P(B∣A)

$= \frac{ P(A∩B)}{P(A)} ​ = \frac{\frac{2}{6}}{\frac{3}{6}}=\frac{2}{3}$