Question

21.Bill and Sam are playing a game where they roll a die and draw a card from a deck. What is the probability of rolling a 5 and then drawing a 5 from the deck of cards? Write your answer as a fraction in lowest terms.

Answer 1

Step-by-step explanation

So we must find the probability that two independent events happen at once. These events are rolling a 5 and drawing a 5 from the deck. Since they are independent events because the result of one of them doesn't depend on the result of the other the probability that both happen is given by the product of their individual probabilities.

The probability of rolling a 5 is given by the quotient between the number of 5's in the die and the total number of faces in the die. There's only one 5 in the die and it has 6 faces so the probability of rolling a 5 is:

`P(r5)=(1)/(6)`

A standard deck has 52 cards and four of those cards are fives. Then the probability of drawing a 5 is given by the quotient between the number of fives in the deck and the total number of cards in it. Then we get:

`P(d5)=(4)/(52)=(1)/(13)`

Then the probability of rolling a 5 and then drawing a 5 from the deck is given by the product of the two probabilities that we found before:

`P=(1)/(6)\cdot(1)/(13)=(1)/(78)`Answer

Then the answer is 1/78.