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Keys, Marbles and Class

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1) You carry five keys in your pocket, two of which are for the two locks on your front door. You lose one key. What is the probability that you can get into your house through the front door? (Enter your answer as a fraction.)

2) Use the given values to find the following. (Enter your answers as fractions.)

P(A) = 0.6,
P(B) = 0.4,
P(A ∩ B) = 0.3
(a) P(A given B)
(b) P(B given A)

3) A box contains 5 white, 3 red, and 4 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)

4) Two students are registered for the same class and attend independently of each other, student A 70% of the time and student B 60% of the time. The teacher remembers that on a given day at least one of them is in class. What is the probability that student A was in class that day? (Round your answer to three decimal places.)

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Solution Summary

Answered in 325 words. Step-by-step computations are shown. Formulas are probided.

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1)
The two locks on your front door are different locks, and hence two different keys are needed simultaneously to open the front door.

Since 2 of the keys are needed for the front door, that means that 3 of the keys are not needed for the front door.
The probability that you can get into the house through the front door is the same as the probability that you did not lose the ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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  • "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
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