Question

There are 4 cards in the box with the numbers 2, 5, 6, and 8. Two cards are drawn one after the other. The second card drawn is placed to the right of the first card. In this way obtaining a two-digit number. 1) List all the numbers so available. 2) Calculate the probabilities of events:A - the obtained number is even; B - the obtained number is a multiple of 5;C - the number obtained is a multiple of 3.

Answer 1

It is given that there are 4 cards with numbers 2, 5, 6, and 8.

1) It is required to list all the numbers available when two cards are drawn one after the other and the second card is placed at the right of the first card drawn.

To do this, find the sample space of the draw which are:

$25,26,28,52,56,58,62,65,68,82,85,86$

Hence, the required numbers.

2) Recall that probability is the ratio:

$Probability=\frac{\text{ number of favorable outcomes}}{\text{ total number of possible outcomes}}$

From the numbers listed, notice that the total number of possible outcomes is 12.

Since event A is "obtained number is even", notice that the number of even numbers in the listed numbers is 9 (26,28,52,56,58,62,68,82,86).

Hence, the number of favorable outcomes is 9.

Substituting into the probability ratio gives the required probability:

$P(A)=\frac{9}{12}=\frac{3}{4}$

Check the number of numbers that are a multiple of 5, notice that they are 3 (25,65,85).

Hence, the required probability of event B is:

$P(B)=\frac{3}{12}=\frac{1}{4}$

The number of multiple of 3 in the listed numbers is 0 since there is no number that is a multiple of 3.

Hence, the required probability of event C is:

$P(C)=\frac{0}{12}=0$

Answers:

1) {25,26,28,52,56,58,62,65,68,82,85,86}

2) P(A) = 3/4

P(B) = 1/4

P(C)= 0