Question

If you roll one die and flip one coin, what is the probability of rolling a 2 and flipping a head? Why?

Answer 1

The probability of rolling a 2 and flipping a head is
`(1)/(12)`

Explanation:

Notice that rolling a die and flipping a coin are two independent events this means that the probability that one event occurs in no way affects the probability of the other event occurring. When we determine the probability of two independent events we multiply the probability of the first event by the probability of the second event.

`P(X and \:Y) =P(X) \cdot P(Y)`

When you roll a die there six outcomes from 1 to 6 and when you flip a coin are two possible outcomes (heads or tails).

We know that the probability of an event is

`P=(the \:number \:of \:wanted\:outcomes)/(the \:number \:of \:possible \:outcomes)`

So the probability of rolling a 2 and flipping a head is

`P(2 \:and \:H) = P(2) \cdot P(H)\\P(2 \:and \:H) = (1)/(2) \cdot (1)/(6)\\P(2 \:and \:H) = (1)/(12)`

Answer 2

Probability of rolling a 2 and flipping a head will be
`(1)/(12)`

Explanation:

If we roll one die then probability to get any one side is
`(1)/(6)`

Therefore, probability to get 2 by rolling the die will be P(A) =
`(1)/(6)`

Now we flip a coin then getting head or tale probability is
`(1)/(2)`

Or probability to get head by flipping the coin P(B) =
`(1)/(2)`

Probability of happening both the events (rolling a 2 and flipping a head) will be denoted by

P(A∩B) = P(A)×P(B)

=
`(1)/(6)* (1)/(2)`

=
`(1)/(12)`

Therefore, probability of rolling a 2 and flipping a head will be
`(1)/(12)`