Question

Connor randomly chooses a card from a deck of numbered cards. the cards are numbered 1 through 10, and each number appears only one time. What is the probability that the card Connor chooses has a number on it that is even or divisible by 5?

1) 7/10
2) 3/5
3) 1/2
4) 4/5

Answer 1

Probability that the card Connor chooses has a number on it that is even or divisible by 5 is (3/5) or 0.6.

Explanation:

We are given that Connor randomly chooses a card from a deck of numbered cards. the cards are numbered 1 through 10, and each number appears only one time.

And we have to find the probability that the card Connor chooses has a number on it that is even or divisible by 5.

Let the Probability that card Connor chooses has a number on it that is even = P(A)

Probability that card Connor chooses has a number on it that is divisible by 5 = P(B)

Probability that card Connor chooses has a number on it that is even and divisible by 5 =
`P(A\bigcap B)`

Probability that card Connor chooses has a number on it that is even or divisible by 5 =
`P(A\bigcup B)`

Here, Even numbers are = {2, 4, 6, 8, 10} = 5

Numbers divisible by 5 = {5, 10} = 2

Also, Number which is even and also divisible by 5 = {10} = 1

Total numbers = 10

Now, Probability that card Connor chooses has a number on it that is even =
`(5)/(10)` = 0.5

Probability that card Connor chooses has a number on it that is divisible by 5 =
`(2)/(10)` = 0.2

Probability that card Connor chooses has a number on it that is even and divisible by 5 =
`(1)/(10)` = 0.1

Now,
`P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)`

= 0.5 + 0.2 - 0.1

= 0.6 =
`(3)/(5)`

Hence, probability that the card Connor chooses has a number on it that is even or divisible by 5 is 0.6.