Answer:
Probability that the card Connor chooses has a number on it that is even or divisible by 5 is (3/5) or 0.6.
Step-by-step 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 = [tex]P(A\bigcap B)[/tex]
Probability that card Connor chooses has a number on it that is even or divisible by 5 = [tex]P(A\bigcup B)[/tex]
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 = [tex]\frac{5}{10}[/tex] = 0.5
Probability that card Connor chooses has a number on it that is divisible by 5 = [tex]\frac{2}{10}[/tex] = 0.2
Probability that card Connor chooses has a number on it that is even and divisible by 5 = [tex]\frac{1}{10}[/tex] = 0.1
Now, [tex]P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)[/tex]
= 0.5 + 0.2 - 0.1
= 0.6 = [tex]\frac{3}{5}[/tex]
Hence, probability that the card Connor chooses has a number on it that is even or divisible by 5 is 0.6.
