QuestionInis question: 3 point(s)
possible
Submit quiz
For the experiment of drawing a single card from a standard 52-card deck, find (a) the probability of the given event, and (b) the oc in favor of the given event.
not a four
(a) The probability is
(Type an integer or a simplified fraction.)
(b) The odds, in simplified form, in favor of the event of the card not being a four, are to .
Studdy Solution
STEP 1
1. A standard deck of cards has 52 cards.
2. There are 4 cards that are fours in a standard deck (one for each suit: hearts, diamonds, clubs, spades).
3. Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
4. Odds in favor are calculated as the ratio of favorable outcomes to unfavorable outcomes.
STEP 2
1. Calculate the probability of drawing a card that is not a four.
2. Calculate the odds in favor of drawing a card that is not a four.
STEP 3
Calculate the total number of cards that are not fours.
There are 4 fours in the deck, so the number of cards that are not fours is:
STEP 4
Calculate the probability of drawing a card that is not a four.
The probability is given by:
Simplify the fraction:
STEP 5
Calculate the odds in favor of drawing a card that is not a four.
The odds in favor are given by the ratio of favorable outcomes to unfavorable outcomes.
Favorable outcomes: 48 (not a four)
Unfavorable outcomes: 4 (a four)
The odds are:
Simplify the ratio:
The probability of drawing a card that is not a four is:
The odds in favor of drawing a card that is not a four are:
Was this helpful?
