One card is selected at random from an ordinary set of 52
cards. Find the probability of each of the following events:
b. A spade and a 5 are drawn.
d. A jack is not drawn
Well, you are only drawing one card. Therefore if it is a spade and a five it is the five of spades so 1/52
48/52 of the cards are not Jacks.
thank you. i understand how you got 48/52 since there are 4 jacks but do i need to simplify the answer?
yes, simplify
To find the probability of each event, we need to know the total number of possible outcomes and the number of favorable outcomes for each event.
a. A spade and a 5 are drawn:
In a deck of 52 cards, there are 13 spades (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King), and only one of them is a 5 of spades. Therefore, the number of favorable outcomes is 1.
The total number of possible outcomes is still 52 (there are 52 cards in the deck).
The probability of drawing a spade and a 5 is:
P(A spade and a 5) = Number of favorable outcomes / Total number of possible outcomes
= 1 / 52
= 1/ 52 (approximately 0.019 or 1.9%)
b. A jack is not drawn:
In a deck of 52 cards, there are 4 jacks (one in each suit - hearts, diamonds, clubs, and spades). To calculate the number of outcomes where a jack is not drawn, we subtract the number of jacks from the total number of cards.
The number of favorable outcomes is 52 - 4 = 48 (not drawing a jack).
The total number of possible outcomes remains 52 (there are still 52 cards in the deck).
P(A jack is not drawn) = Number of favorable outcomes / Total number of possible outcomes
= 48 / 52
= 12 / 13 (approximately 0.923 or 92.3%)