If a single card is drawn at random from a shuffled deck, what is the probabilit

Question

If a single card is drawn at random from a shuffled deck, what is the probability that it will be a jack or a queen an ace or a red card If a die is tossed three times, what is the probability of getting one six anything but a six on every toss at least one six If three cards are drawn with replacement from a shuffled deck, what is the probability that all three will be aces none of the three will be aces at least one of them will be an ace Calculate the probabilities in #3 if each card is not replaced after it is drawn. A reception was held for local men and women who own either a large business or a small business. There are 200 people in the room: 50 of the people own a large business, 80 of the people are women, and 90 of the people are men who own a small business. Prepare a joint frequency table of the data. Make sure the numbers in each cell and the totals in the margins are whole numbers. Label the table appropriately. Prepare a joint probability table for the data. Be sure to include marginal probabilities. Suppose that you randomly select one person in the room, what is the probability that the person is a male? Suppose that you randomly select one person in the room. What is the probability that the person is a female small business owner? Suppose that you randomly select one person in the room, given that the person owns a large business, what is the probability that the person is a man? If p(A) = .50, p(B)_ = .30, and p(A and B) = .15: Are A and B mutually exclusive events? Why or why not? Are A and B independent events? Why or why not?

Explanation / Answer

1) In standard deck cards total number of cards are 52.

And in 52 cards there are 4 jack and 4 queen .

a) P( jack or queen)=p(jack)+p(queen)-p( jack and queen)

p(jack and queen)=0 because both cards are desjoints .

p(jack or queen)=p(jack)+p(queen)=4/52+4/52=8/52=2/13

Final answer of a) 2/13

b) p(ace or red)=p(ace)+p(red)-p( ace and red)

4 ace in 52 cards

p(ace)=4/52

26 cards are red in 52 cards.

p(red)=26/52

And in 26 red cards there are 2 cards are ace .

p(ace and red)=2/52

So,

p(ace or red)=4/52+26/52-2/52

=28/52

Final answer of b) 28/52

6)

p(A)=0.50 , p(B)=0.30,p(A and B)=0.15

a) If A and B are mutually exclusive events then P( A and B)=0

But here P(A and B) not equal to 0 .

A and B not mutually exclusive events .

b)

If A and B are independent then P(A and B)=P(A) *P(B)

P(A and B)=0.15

P(A)*P(B)= 0.50*0.30=0.15

So, from above probability.

P(A and B)=P(A)*P(B)=0.15

A and B are independent events .

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