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A particularly bad software crashes approximately 9 out of 10 times that it is used, with...

A particularly bad software crashes approximately 9 out of 10 times that it is used, with each use being independent of others. a. What is the probability that the software will crash the first time you use it? b. What is the probability it crashes for the first time on your third use of it? c. What is the probability that the first time it crashes will be on or after your third use?

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Answer #1

(a) P(crash in 1st time) = P(crash) = 9/10

(b) P(crashes first time in 3rd use) = P(does not crash in 1st use)*P(does not crash in 2nd use)*P(crash in 3rd use)

= (1/10)*(1/10)*(9/10)

= 9/1000

  P(crashes first time in 3rd use) = 0.009

(c) Basically meaning of "first time it crashes will be on or after your third use" is that the software doesnt crash in the first 2 uses

P(crashes first time in 3rd use or after 3rd use) = P(doesn't crash in first two uses)

= P(does not crash in 1st use)*P(does not crash in 2nd use)

= (1/10)*(1/10)

= 1/100

P(crashes first time in 3rd use or after 3rd use) = 0.01

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