Question

A spinning wheel has the following numbers.

(There are 1-8 numbers in the wheel)

Cathy spins the wheel and tosses a coin simultaneously.

Find the following probabilities:

Getting a 7 and tails.
Getting a prime number and heads.
Getting a number greater than 5 and tails.

Answer 1

`(1)/(16), (1)/(4), (3)/(16)`

Explanation:

Recall a probability:
`P=(F)/(T)` , where F is a number of favorable outcomes and T is a number of total outcomes.

The probability to get tail is
`(1)/(2)` as well as probability to get head.

The probability to choose number 7 of 8 numbers at total is equal to
`(1)/(8)`.

Therefore, the probability to get number 7 and a tail is:

`(1)/(8)\cdot (1)/(2)=(1)/(16)`

Prime numbers from 1 to 8 are: 2, 3, 5 and 7, so there are 4 numbers of 8 numbers in total, so the probability to get a prime number is
`(4)/(8)=(1)/(2)`.

The second probability is equal to
`(1)/(2)\cdot (1)/(2)=(1)/(4)`.

The numbers greater than 5 are: 6,7,8, so there are 3 numbers of 8 in total, so the probability to get a number greater than 5 is
`(3)/(8)`.

The third probability is equal to:
`(3)/(8)\cdot (1)/(2)=(3)/(16)`.