SOLUTION: reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each. if she choose two of these coons at random, what is the probability that the two coins together will be worth
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Question 1059726: reyna has 5 coins worth 10 cents each and 4 coins worth 25 cents each. if she choose two of these coons at random, what is the probability that the two coins together will be worth at least 35 cents? Found 2 solutions by Fombitz, Theo:Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! Let D be the 10 cent coin, let Q be the 25 cent coin.
Look at the possible outcomes of a two coin draw and the sums,
DD=>20
DQ=>35
QD=>35
QQ=>50
Look at the probability of each outcome (I wont simplify until the final answer),
DD:
DQ:
QD:
QQ:
When you sum the probabilities, they add up to 1 so all possible outcomes are covered.
So for at least 35, sum the probabilities where the sum is at least 35.
she would need to pick two coins that are worth at least 35 cents.
that could be 1 ten cent coin and 1 twenty five cent coin, or it could be 2 twenty five cent coins.
once she picks the first coin, she does not put it back in the pot.
the probability is therefore without replacement.
the probability of picking a ten cent coin and a twenty five cent coin is:
5/9 * 4/8 plus 4/9 * 5/8
5/9 * 4/8 assumes she picked a ten cent coin first and then a twenty five cent coin.
4/9 * 5/8 assumes she picked a twenty five cent coin first and then a ten cent coin.
the probability of picking a twenty five cent coin and another twenty five cent coin is 4/9 * 3/8.
the total probability is therefore 5/9 * 4/8 plus 4/9 * 5/8 plus 4/9 * 3/8.
this is equal to 20/72 + 20/72 + 12/72 which is equal to 52/72.
she will not get at least 35 cents when she first picks a ten cent coin and then another ten cent coin.
in the tree diagram shown below, that would be the left branch.
the sum of all probabilities must be equal to 1.
the total probability is 1 as it should be.
3 * 20/72 + 12/72 = 72/72 which is equal to 1.
all branches are good except for the left branch.
the left branch will only get get 20 cents which is less than 35 cents (ten + ten).
the 3 other branches will all get her at least 35 cents.
2 of those 3 branches will get her 35 cents (ten + twenty five, twenty five + ten).
the third of those 3 branches will get her 50 cents (twenty five + twenty five).
the boxes in the diagram show what's in the pot.
the name of the branches show what coin was taken out of the previous pot.
you should be able to draw a tree diagram that visualizes this situation.
