SOLUTION: Mario and Bowser begin with a hat that has 5 balls in it: 3 are red, 2 are green. Bowser secretly picks a ball and tells Mario it is red, although he might be lying about the color

Question 1043824: Mario and Bowser begin with a hat that has 5 balls in it: 3 are red, 2 are green. Bowser secretly picks a ball and tells Mario it is red, although he might be lying about the color. If there is an 80% chance Bowser is lying, what is the probability that Mario draws 2 red balls in a row after Bowser's initial draw?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
hat has 5 balls in it.
3 are red and 2 are green.
bowser takes a ball out and says it's red.

80% chance bowser is lying.
20% chance bowser is telling the truth.

what is the probbility that mario will get 2 balls out of the hat that are both red?

probabilities and percentages are linked together in that, if something occurs 80% of the time, then the probability that it will occur the next time is 80%.

the inherent assumption is that, if the probability is 80%, then if you repeat the experiment an infinite number of times, the frequency of occurrence will be 80% as well.

flip a coin is an example.
the probability of getting heads in a fair coin is 50%.
if you flip the coin an infinite number of times, heads will come up 50% of the time.

same type of thing happens with this.

80% of the time bowser is lying, so 80% of the time there will be 3 red balls and 1 green ball in the hat after he draws a ball out of it.
the probability of getting 2 red balls in a row will be 3/4 * 2/3 = 6/12 = 1/2.

20% of the time bowser is telling the truth, so 20% of the time there will be 2 red balls and 2 green balls in the hat after he draws a ball out of it.
the probability of getting 2 red balls in a row will be 2/4 * 1/3 = 2/12 = 1/6.

80% = 8/10 = 4/5
20% = 2/10 = 1/5

the total probability is (4/5 * 1/2) + (1/5 * 1/6) = 4/10 + 1/30 = 12/30 + 1/30 = 13/30.

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