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.


Our club elections are tomorrow. How many different ways can president, vice

president, secretary and treasurer been chosen from 8 students? (D1b)

a) 8 b) 70 c) 1680 d) 4096

b) so you are picking the 5 of spades

so prob(5 of spades) = 1/52

d) prob (of a jack) = 4/52 = 1/13

then prob(not a jack) = 1 - 1/13 = 12/13

Please post your question in a new post, not as a reply to somebody else's.

There are 8 ways to pick a president, then 7 ways to pick a vp, then 6 ways for the treasurer , and 5 ways for the secretary.

So the number of ways = 8x7x6x5 = 1680

To find the probability of each event, we need to determine the total number of favorable outcomes and divide by the total number of possible outcomes.

a. A spade and a 5 are drawn:
To count the favorable outcomes, we need to figure out how many spade cards there are in the deck, which is 13 (since there are 13 of each suit in a standard deck of cards). We also need to determine how many 5 cards there are in the deck, which is 4 (one for each suit).

Since we want to find the probability of drawing both a spade and a 5, we need to find the number of cards that satisfy both conditions. There is only 1 card in the deck that is both a spade and a 5, namely the 5 of spades.

Therefore, the number of favorable outcomes is 1.

Now, let's determine the total number of possible outcomes. Since there are a total of 52 cards in the deck, the total number of possible outcomes is 52.

To find the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 1/52.

b. A jack is not drawn:
To count the favorable outcomes, we need to figure out how many cards in the deck are not jacks. There are 4 jacks in the deck, so we subtract 4 from the total number of cards to get the number of cards that are not jacks, which is 52 - 4 = 48.

Therefore, the number of favorable outcomes is 48.

Now, let's determine the total number of possible outcomes. Since there are a total of 52 cards in the deck, the total number of possible outcomes is 52.

To find the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 48/52 = 12/13.