SOLUTION: 1) there are 3 cards in a hat; one is a king,one is a queen and one is an ace. two cards are to be selected at random with replacement using a tree diagram, obtain a smample space

Question 183136: 1) there are 3 cards in a hat; one is a king,one is a queen and one is an ace. two cards are to be selected at random with replacement using a tree diagram, obtain a smample space for the experiment. then find the probaiblty that a queen and king are selected?
2) assume that a person spins a spiner and is awarded the amount indicated by the pointer. detrimine the persons expection.
4 parts
2-$8
1-$12
1- $1
3) one card is selected from a deck of cards. find the probabilty of selecting a red card or a card less then 4. (note: the ace is a low card)
4) a number cube labeled with numbers 1-6 is tossed. what are the odds of the number being less than 3.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1) there are 3 cards in a hat; one is a king,one is a queen and one is an ace. two cards are to be selected at random with replacement using a tree diagram, obtain a smample space for the experiment. then find the probaiblty that a queen and king are selected?
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Sample Space:
1st level of the tree: k,q,a
2nd level of the tree: k,q,a paired with each element of the 1st level
(you now have 3*3 = 9 branches
3rd level of the tree: k,q,a paired with each element of the 2nd level
(you now have 3*3*3 = 27 branches)
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Your Problem:
P(k and q selected in 1st two draws) = 2/9
(they are kq and qk)
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2) assume that a person spins a spinner and is awarded the amount indicated by the pointer. determine the persons expected value.
4 parts
2-$8
1-$12
1- $1
----------
Random variable values : 8, 12, 1
Corresponding Probabilities:
P(8) = 2/4 = 1/2
P(12) = 1/4
P(1) = 1/4
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Multiply each random variable value by it propability and add the products
to get the expected value:
E(x) = 8*(1/2) + 12*(1/4) + 1*(1/4) = 4 + 3 + 0.25 = $7.25
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3) one card is selected from a deck of cards. find the probabilty of selecting a red card or a card less then 4. (note: the ace is a low card)
P(red or < 4) = P(red) + P(< 4) - P(red AND < 4)
= 1/2 + 12/52 - (6/52) = 32/52 = 8/13
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4) a number cube labeled with numbers 1-6 is tossed. what are the odds of the number
--------
You did not include the number in your posting.
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But if it is ANY particular number proceed as follows:
odds for the number = P(the number) / P(not getting the number)
= (1/6)/(5/6) = 1/5
odds for the number are 1:5
================================
Cheers,
Stan H.
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