Question

Milan uses a probability simulator to roll a six-sided number cube 100 times and to flip a coin 100 times. The results of the experiment are shown below:

Number on the Cube Number of Times Rolled
1 10
2 8
3 33
4 29
5 11
6 9


Heads Tails
29 71


Using Milan's simulation, what is the probability of rolling a 5 on the number cube and the coin landing on tails?

Answer 1

rolling a 5= 11/100

getting tails=71/29

i’m pretty sure you times the fractions together to get an overall probability

Answer 2

The probability of rolling a 5 on number cube and tail on coin is:

`P(A\bigcap B)=(781)/(10000)`

or

`P(A\bigcap B)=0.0781`

Explanation:

Let A denote the event of rolling a 5 on the number cube.

and B denote the event of coin landing on tails.

Let P denote the probability of an event.

Also, event A is independent of event B.

( Since, both the events are not affected by happening of each other )

We are asked to find the probability: P(A∩B)

We know that:

`P(A\bigcap B)=P(A)\cdot P(B)`

( Since, both the events are independent )

Also,

`P(A)=(11)/(100)`

( Since, 5 occurs 11 times out of a total of 100 times on the number cube )

and

`P(B)=(71)/(100)`

Hence, we have:

`P(A\bigcap B)=(11)/(100)* (71)/(100)`

i.e.

`P(A\bigcap B)=(781)/(10000)`

i.e.

`P(A\bigcap B)=0.0781`