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Probability questions with cards, Tree diagrams vs Tables

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1. If an ace has a face value of one, a 2 has a value of two, a Jack has a value of 11, and so on for all of the cards, what is the probability of drawing a card that has a face value of less than six?

2.
A friend tells you that a tree diagram can be used to generate the sample space for any experiment, but a table or grid can not.
(a) Is this true?

(b) Use examples to explain your response in part (a).

3.
A card is drawn form a standard deck of playing cards, returned to the deck, and then a second card is drawn. Determine the following probabilities:
a. Both cards are aces or both cards are face cards.

b. Both cards are red or both cards are face cards

Solution Preview

Dear Student,

I am including the solution to these questions below.

Best of Luck.

OTA 103881

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1. If an ace has a face value of one, a 2 has a value of two, a Jack has a value of 11, and so on for all of the cards, what is the probability of drawing a card that has a face value of less than six?

There 13 possible values for cards.

Ace = 1.

2, 3, 4, 5, 6, 7, 8, 9, 10 for the numbered cards.

Jack = 11, Queen =12, King = 13.

Less than 6 means cards can be Ace or 2 or 3 or 4 or 5. Thus, there are 5 possible values.

Probability of face value less than 6 = 5/13

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2. A friend tells you that a tree diagram can be used to generate the sample space for any experiment, but a table or grid can not.
(a) Is this true?
No. This is not true. A tree diagram is only a convenient way to visualize all the outcomes in a sample space. This can also be done using a table but may be more ...

Solution Summary

Probability distribution of 2 or multiple cards drawn without replacement from a pack

Tree diagram vs Table/Grid

$2.19