Question

you flip a coin and use a random number generator to generate a number from 1 to 10 what is the probability that the coin shows heads and the number is two

Answer 1

INFORMATION:

We know that:

- you flip a coin and use a random number generator to generate a number from 1 to 10

And we must find the probability that the coin shows heads and the generated number is two

STEP BY STEP EXPLANATION:

To find the probability, we need to use that we have two independent events. First, flip a coin and second, generate a number from 1 to 10. They are independent events because their occurrence is not dependent on any other event.

So, to calculate the probability, we need to use the formula for compound probability of independent events

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

In this case:

- A represents the event of flip a coin

- B represents the event of generate a number from 1 to 10

Now, we must calculate P(A) and P(B)

`P(A)=\frac{favorable\text{ }cases}{total\text{ }cases}=(1)/(2)`
`P(B)=\frac{favorable\text{ }cases}{total\text{ }cases}=(1)/(10)`

Then, knowing that P(A) = 0.5 and P(B) = 0.1 we need to replace their values in the initial formula

`P(A\cap B)=0.5\cdot0.1=0.05`

ANSWER:

The probability that the coin shows heads and the number is two is 0.05