Question

lewis rolls a number cube and then chooses a card from a set of cards numbered 1 through 5. What is the probability that he will roll an evennumber and choose an even numbererd card?

Answer 1

Answer:

The probability that he will roll an even number and choose an even numbered card is 1/5.

P(Xe∩Ye) = 1/5 or 0.2

Step-by-step explanation:

Let X represent the possible outcomes of the number cube. And Y represent the possible outcomes of the cards.

X = {1,2,3,4,5,6}

n(X) = 6

Y = {1,2,3,4,5}

n(Y) = 5

The number of possible even outcomes of the number cube is;

Xe = {2,4,6}

n(Xe} = 3

The number of possible even outcomes of the card is;

Ye = {2,4}

n(Ye) = 2

The probability that he will roll an even number and choose an even numbered card can be written as;

P(Xe∩Ye) = P(Xe) × P(Ye) .......1

P(Xe) = n(Xe)/n(X) = 3/6 =1/2

P(Ye) = n(Ye)/n(Y) = 2/5

Substituting into equation 1, we have;

P(Xe∩Ye) = 1/2 × 2/5

P(Xe∩Ye) = 1/5 or 0.2

Answer 2

Answer:

$\frac{1}{5}$

Step-by-step explanation:

Sample Space for the Cube, A={1,2,3,4,5,6}

n(A)=6

Even Numbers in A={2,4,6}

Sample Space for the Cards, B={1,2,3,4,5}

n(B)=5

Even numbers in the card,B= {2,4}

The two events are INDEPENDENT Events as the outcome of the cube does not affect the card picked, therefore:

P(A and B)=P(A) X P(B)

=$\frac{3}{6} X \frac{2}{5}$

=$\frac{1}{5}$