You have a 4-card deck containing a queen, a jack, a 10, and a 9. You draw a random card, put it back, and draw a second random card. Use a tree diagram to calculate the probability that you draw exactly 1 face card (a queen or a jack).
A. 1/2.
B. 7/16.
C. 1/4.
D. 9/16.
To calculate the probability of drawing exactly 1 face card, we need to consider the possible outcomes for each draw and their probabilities.
First, let's create a tree diagram to visualize the possible outcomes:
-----------------
| |
Queen (Q) Non-Face Card (NFC)
| |
--------------- N
| |
Jack (J) Non-Face Card (NFC)
| |
--------------- N
| |
10 (10) Non-Face Card (NFC)
| |
--------------- N
| |
9 (9) Non-Face Card (NFC)
| |
--------------- N
In this tree diagram, Q represents a face card (queen), J represents a face card (jack), and NFC represents a non-face card (10 or 9). N represents a non-face card being drawn in the second round.
Now, let's calculate the probability for each outcome:
P(Q) = 1/4 (there is one queen in the deck)
P(J) = 1/4 (there is one jack in the deck)
P(NFC) = 2/4 = 1/2 (there are two non-face cards in the deck)
P(N) = 4/4 = 1 (regardless of the first draw, there are four remaining cards)
To calculate the probability of drawing exactly 1 face card, we can multiply the probabilities of different branches in which only one face card is drawn:
P(1 face card) = (P(Q) * P(NFC)) + (P(J) * P(NFC))
= (1/4 * 1/2) + (1/4 * 1/2)
= 1/8 + 1/8
= 2/8
= 1/4
Therefore, the probability of drawing exactly 1 face card is 1/4.
So, the correct answer is C. 1/4.
I cannot draw a tree diagram here.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Face card = 2/4 = 1/2
Non-face card = 2/4 = 1/2