A single card is drawn from a standard deck of cards. Find the following probabilities. A face card is a jack, queen, or king.
P(face card | queen) = Correct: Your answer is correct.
P(three | not a face card)
Conditional probability
P(A|B) is defined as
P(A|B)=P(A∩B)/P(B)
Hence:
P(face card | queen)
=P(face card ∩ queen)/P(queen)
=P(queen)/P(queen)
=1
P(three|not a face card)
=P(three ∩ not a face card)/P(not a face card)
=(4/52)/(40/52)
=1/10
To find the probability of drawing a three given that it is not a face card, we need to consider the number of favorable outcomes (drawing a three) and the number of total outcomes (drawing a card that is not a face card).
First, let's determine the number of favorable outcomes. In a standard deck of cards, there are four threes: the three of hearts, three of diamonds, three of clubs, and three of spades. Since we are looking for a three and not a face card, we only consider these four cards.
Next, let's determine the number of total outcomes. We know that a standard deck of cards has 52 cards. To calculate the number of cards that are not face cards, we subtract the number of face cards (12) from the total number of cards.
Total number of cards that are not face cards = Total number of cards - Number of face cards
= 52 - 12
= 40
Therefore, the number of total outcomes is 40.
Now, we can calculate the probability of drawing a three given that it is not a face card:
P(three | not a face card) = (Number of favorable outcomes) / (Number of total outcomes)
= 4 / 40
= 1 / 10
= 0.1
= 10%
So, the probability of drawing a three given that it is not a face card is 1/10 or 10%.