Question

A 6-sided die rolled twice. Let E be the event "the first roll is a 5" and F F the event "the second roll is a 5".

(a) Are the events E E and F F independent?

Input Yes or No:

(b) Find the probability of showing a 5 on both rolls.

Write your answer as a reduced fraction. Answer:

Answer 1

Answer 2

ANSWERS :

a.  Yes 

(Events E and FF are independent.

Getting 5 on second roll (event FF)  is not dependent on getting 5 on the first roll (event E). Hence, these events are independent.)

b. 

On first roll,  6 outcomes are possible : 1, 2, 3, 4, 5, 6 . 

Getting 5 is one outcome.

Hence, P(5 on first roll) = P(E) = 1/6 

Similarly, P(5 on second roll) = P(FF) = 1/6 

P( both rolls show 5) 

= P(5 on first roll) * P(5 on second roll)  (Since events are independent)

= P(E) * P(FF)

= 1/6 * 1/6

= 1/36 (ANSWER).