1. Using the formula for the probability of one event or another event, calculate the probability of drawing a card from a stand
ard deck that is either a jack or a club. Write out the formula and show your work. Write the final answer as a fraction in simplified form. (10 points) Bonus question for extra credit: What is the probability of drawing two cards from a deck, without replacing the first card, and either getting two red cards or two aces? Hint: the probability of getting two aces is the probability of the first card being an ace, times the probability of the second card being a different ace. Show your work, and write your answer as a fraction in reduced form.
A standard deck has 52 cards. A standard deck has 4 jacks. A standard deck has 13 clubs.
From this, we can derive the following: The probability of drawing a jack is 4/52 or 1/13 The probability of drawing a club is 13/52 or 1/4
But since the problem asks for drawing jack or club, therefore we should add the 2 probabilities, making 17/52. This is not the final answer yet. We know that there is a jack of clubs, therefore we need to subtract 1 from the probabilities since jack of clubs were considered in the 2 categories of probability.
With that being said, the probability of drawing a club or a jack is 16/52 or 4/13
Bonus Question:
The first thing you need to do here is find the probability of each scenario. First let's do what is given, the probability of drawing 2 aces. Since there are 4 aces in a deck of 52, we can easily say that the probability of drawing an ace is 4/52. However for our second draw, the probability of drawing a different ace is 3/51. This is so since we already drew a card that is an ace, hence we need to subtract one from the total aces (4-1) and from the total cards in the deck (52-1). In getting the probability of drawing two aces, we need to multiply the said probabilities: 4/52 and 3/51, resulting to 1/221. For the second scenario, the drawing of 2 red cards, we just use the same concept but in this, we are already considering the 2 red cards in the first scenario, therefore the chance of drawing a red on our first draw is 24/52. For our second, we just need to subtract one card, therefore 23/51. Multiply these two and we will get 46/221. Now, the problem asks for the chance of drawing either 2 reds or 2 aces, therefore we add the probabilities of the 2 scenarios: 46/222 + 1/221 = 47/221
Summary: First Scenario: 4/52 + 3/51 = 1/221 Second Scenario: 24/52 + 23/51 = 46/221 Chances of drawing 2 red cards or 2 aces: 1/221 + 46/221 = 47/221
Old Faithful is a famous geyser at Yellowstone National Park. From a sample with n = 32, the mean duration of Old Faithful's eruptions is 3.32 minutes and the standard deviation is 1.09 minutes. Using Chebychev's Theorem, determine at least how many of the eruptions lasted between 1.14 minutes and 5.5 minutes.