A card is drawn from a standard deck. What is the probability that the card is less than 7, given that the card is not a face card? (Assume that ace is high, and that aces are not face cards.)
A: .4165
B: .3846
C: .2959
D: .6
E: .5
F: None of these
The answer is B, there are 5 cards less than 7 in a standard deck, (assuming that ace is high) 2, 3, 4, 5, 6. There are 13 cards of each suit in the deck. So 5/13 will give us 0.3846.
To find the probability that a card is less than 7, given that it is not a face card, we first need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the number of favorable outcomes. Since we are considering cards that are less than 7, the favorable outcomes are the cards numbered 2, 3, 4, 5, and 6. There are a total of 5 favorable outcomes.
Next, let's determine the total number of possible outcomes. A standard deck of cards contains 52 cards. Since we are considering cards that are not face cards, we need to subtract the number of face cards from the total. In a standard deck, there are 4 face cards in each suit (jack, queen, and king), so there are a total of 12 face cards. Therefore, the total number of possible outcomes is 52 - 12 = 40.
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes) = 5 / 40 = 1/8 = 0.125
However, the question asks for the probability as a decimal. So, we round the probability to four decimal places:
Probability ≈ 0.125
None of the given choices perfectly matches this value, but the closest option is C: 0.2959.