A card is drawn at random from an ordinary deck of playing cards. Find the following odds.
A. Odds in favor of drawing a 5,6,7
B. Odds against drawing a king, queen, jack, or ace
D.Odds against drawing an even numbered (2,4,6,8,10)card.
Can I get some help with this question please.
there are 12 cards which are either 5,6, or 7
so Prob (a 5,6,or7) = 12/52 = 3/13
so prob (not a 5,6,or7 ) = 10/13
Odds in favour of a 5,6,or7 = (3/13)/(10/13) = 3/10
or 3 : 10 , the usual way of stating odds
Now try the others the same way, let me know what you get
To solve this question, we need to first determine the total number of cards in a deck. An ordinary deck of playing cards consists of 52 cards.
A. Odds in favor of drawing a 5, 6, or 7:
To find the odds in favor of drawing a 5, 6, or 7, we need to determine the number of favorable outcomes and the number of unfavorable outcomes. In this case, the favorable outcomes are the 5, 6, and 7 cards, which means there are three favorable cards. The remaining cards (52-3) are the unfavorable outcomes. Therefore, the odds in favor of drawing a 5, 6, or 7 can be expressed as 3:49.
B. Odds against drawing a king, queen, jack, or ace:
Similar to the previous question, we will calculate the number of favorable and unfavorable outcomes. In this case, the unfavorable cards are the king, queen, jack, and ace cards, which means there are 4 unfavorable cards. Consequently, the favorable outcomes are the remaining cards (52-4). Therefore, the odds against drawing a king, queen, jack, or ace can be expressed as 4:48, which simplifies to 1:12.
C. Odds against drawing an even-numbered card:
Again, we calculate the favorable and unfavorable outcomes. For the even-numbered cards (2, 4, 6, 8, 10), there are 5 cards that satisfy this condition. The unfavorable outcomes are the remaining odd-numbered cards, which are 52-5. Thus, the odds against drawing an even-numbered card can be expressed as 5:47.
Remember, the odds in favor of an event are represented as "x:y," where x represents the number of favorable outcomes, and y represents the number of unfavorable outcomes. Conversely, the odds against an event are represented as "x:y," where x represents the number of unfavorable outcomes, and y represents the number of favorable outcomes.