Question 201545: On any given night, Becky has a 60% chance of seeing a shooting star in any given hour. If Becky watches the sky for two hours, find the following probabilities
a. What is the probability that Becky sees a shooting star in both hours?
b. What is the probability that Becky sees a shooting star in exactly one hour?
c. What is the probability that Becky does not see a shooting star at all?
d. Given that Becky did not see a shooting star in the first hour, what is the probability that she will see one in the second hour?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! On any given night, Becky has a 60% chance of seeing a shooting star in any given hour. If Becky watches the sky for two hours, find the following probabilities
These are Binomial problems.
p = 0.6 ; q = 0.4
a. What is the probability that Becky sees a shooting star in both hours?
n = 2 ; = 0.6 ; x = 2
P(x=2) = 0.6^2 = 0.36
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b. What is the probability that Becky sees a shooting star in exactly one hour?
P(x = 1) = 1 - [P(x=0) + P(x=2)] = 1 - (0.4)^2 - 0.6)^2 = 1 -0.16 - 0.36 = 0.48
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c. What is the probability that Becky does not see a shooting star at all?
P(x=0) = 0.4^2 = 0.16
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d. Given that Becky did not see a shooting star in the first hour, what is the probability that she will see one in the second hour?
The events are independent:
P(x = 1 in the 2nd hour) = 0.6
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Cheers,
Stan H.
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