One card is selected at random from an ordinary set of 52 cards. Find the probability of each of the following events:
a spade and a 5 are drawn.
a jack is not drawn.
Thanks for any help with this.
(1) The five of spades is one card out of 52. Hence the answer is 1/52
(2) There are 4 jacks in a deck.
Hence: 4/52 = 1/13
(3) 48 cards of the deck are not jacks. What do you think the answer is?
To find the probability of each event, we need to first determine the number of favorable outcomes (the successful outcomes) and the total number of possible outcomes.
a) Probability of drawing a spade and a 5:
In an ordinary deck of 52 cards, there are 13 spades and 4 fives. Since we want to draw both a spade and a 5, we multiply the number of spades and the number of fives together to get the number of favorable outcomes: 13 * 4 = 52.
The total number of possible outcomes is simply the total number of cards in the deck, which is 52.
So the probability of drawing a spade and a 5 is given by:
P(Spade and 5) = Number of favorable outcomes / Total number of possible outcomes
= 52 / 52
= 1
Therefore, the probability of drawing a spade and a 5 is 1 (or 100%).
b) Probability that a jack is not drawn:
In an ordinary deck of 52 cards, there are 4 jacks. So, the number of favorable outcomes (not drawing a jack) is the total number of cards in the deck minus the number of jacks: 52 - 4 = 48.
Again, the total number of possible outcomes is simply the total number of cards in the deck, which is 52.
So the probability of not drawing a jack is given by:
P(Not Jack) = Number of favorable outcomes / Total number of possible outcomes
= 48 / 52
= 12 / 13
Therefore, the probability of not drawing a jack is 12/13 (or approximately 0.923 or 92.3%).
To find the probabilities of the given events, we need to determine the number of favorable outcomes and the total number of possible outcomes.
a) Probability of drawing a spade and a 5.
- Number of favorable outcomes: There is only one spade that is a 5, which is the 5 of spades.
- Total number of possible outcomes: There are 52 cards in a standard deck.
Therefore, the probability of drawing a spade and a 5 is 1/52.
b) Probability of not drawing a jack.
- Number of favorable outcomes: There are 48 cards that are not jacks (4 suits - 1 jack per suit = 4 * 12 = 48 cards).
- Total number of possible outcomes: Again, there are 52 cards in a standard deck.
Therefore, the probability of not drawing a jack is 48/52, which simplifies to 12/13.
It's worth noting that for the second event, we are assuming that the card is drawn from the deck without replacement, meaning once a card is drawn, it is not put back in the deck before drawing the next card.