Question

Lucia has 50 sports cards. She has 20 football cards, 10 baseball cards, 15 basketball cards and 5 hockey cards. A single card is selected at random. What is the probability that the card is a football card or a basketball card?

John rolls a pair of six-sided number cubes.
What is the probability that the sum of the numbers on the number cubes is either a multiple of 3 or an odd number?

Answer 1

1) 35/50 or simplified it's 7/10 in percent that's 70%
2) 5/6 or 83%

Answer 2

Answer: The probability that the card is a football card or a basketball card is
`(35)/(50)`.

The probability that the sum of the numbers on the number cubes is either a multiple of 3 or an odd number is
`(2)/(3)`

Explanation:

Let A be the event of getting a football card and b be the event of getting a basketball card.

Thus probability of getting a foot ball P(A)=
`(20)/(50)`

The probability of getting a basketball P(B)=
`(15)/(50)`

Selecting a card is a mutually exclusive event , thus probability of getting card is a football card or a basketball card P(A∩B) =P(A)+P(B)

⇒P(A∪B
`=(20)/(50)+(15)/(50)=(35)/(50)`

The probability that the card is a football card or a basketball card is
`(35)/(50)`.

Let E be the event of getting a multiple of 3 and F be the event of getting an odd number.

Then P(A)=
`(2)/(6)`

P(B)=
`(3)/(6)`

P(A∩B)=
`(1)/(6)` [3 is both a multiple of 3 and an odd number]

Thus, P(A∪B)=P(A)+P(B)-P(A∩B)

⇒P(A∪B)
`=(4)/(6)=(2)/(3)`

The probability that the sum of the numbers on the number cubes is either a multiple of 3 or an odd number is
`(2)/(3)`