A consumer organization estimates that over a 1-year period 20% of cars will need to be repaired once, 6% will need repairs twice, and 2% will require three or more repairs. What is the probability that a car chosen at random will need repairs?

1 Answer
Nallasivam V
Apr 14, 2017

Probability of a randomly chosen car need to be repaired#=0.81576#

Explanation:

In one year period

Probability of a randomly chosen car to be repaired once #=20% = 20/100 = 0.2#
Probability of a randomly chosen car not to be repaired once #=1 - 0.2 = 0.8#

Probability of a randomly chosen car to be repaired twice#=6% = 6/100 = 0.06#
Probability of a randomly chosen car not to be repaired twice#=1-0.06=0.94#

Probability of a randomly chosen car to be repaired three or more#=2% = 2/100 = 0.02#
Probability of a randomly chosen car not to be repaired three or more#=1-0.02=0.98#

Probability of a randomly chosen car not to be repaired #=0.2xx0.94xx0.98=0.18424#

Probability of a randomly chosen car need to be repaired = 1 - Probability of a randomly chosen car not to be repaired

#=1-0.18424= 0.81576#

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