Question

Sara rolls a fair dice and flips a fair coin.

a
What is the probability of obtaining a multiple of 3 and a tail?

Answer 1

A dice has 6 sides. or 6 events. A coin has two sides, or 2 events. So using law of counting, we have a total of 12 possibe. events.

Let create a proabliblity function to showcase.

Out of (1,2,3,4,5,6) and (H,T)

We have

1H

1T

2H

2T

3H

3T

4H

4T

5H

5T

6H

6T

A proabliblity function possibilities must add to 1 or 100% Since the dice and coin is fair, and we have 12 possibilities. We do

`(100)/(12) = 8.33333`

So each has 8.333% of occurring or 0.0833. or 100/12

We need to find the proabliblity of Getting a multiple of 3 and a tail.

3 and 6 are multiples of 3 and they get tail one time each so we get

P(3T) +P(6T)= P( proabliblity of getting a multiple of 3 and a tail).

Remeber each possibility has a 100/12 chance of occurring so we have

`(100)/(12) + (100)/(12) = (200)/(12)`

Which equals

`16.6666\%`

So the answer is 16.6666666% or 0.166666

Answer 2

1/6

Explanation:

3 and 6 are the only multiples of 3 on a dice

P(multiple of 3) = 2/6 or 1/3

P(tails) = 1/2

P(mult. 3 and tails) = 1/3 x 1/2 = 1/6