The probability that a person stopping at a certain bank will cash a check is .2

Question

The probability that a person stopping at a certain bank will cash a check is .25 that he or she will make a deposit into a savings 39, and the probability that he or she will do both is .09. What is the probability that a person stopping at this bank will do at least one of the two things mentioned above; neither cash a check nor make a deposit into a savings account; cash a check but not make a deposit into a savings account; cash a check or make a deposit into a savings account, but not both; not cash a check. A box of 10 balls contains 2 red, 3 blue, and 5 green balls. If a ball is from the box in such a manner that each ball has equal probability of being drawn, and if R, B, and G are the events of drawings, a red, blue, and green ball, respectively, then what is P(R); P(B); P(R B); P(R B G); P(B G); P(R' B') P(B' G').

Explanation / Answer

3) Given,

P(Cash a check) = 0.25

P(Deposit) = 0.39

P(Cash a check and deposit) = 0.09

a) P(Cash a check or deposit) = P(Cash a check) + P(Deposit) - P(Both) = 0.25 + 0.39 - 0.09 = 0.55

b) P(Neither cash a check nor deposit) = 1 - P(Cash a check or deposit) = 1 - 0.55 = 0.45

c) P(Cash a check but not make a deposit) = P(Cash a check) - P(Both) = 0.25 - 0.09 = 0.16

d) P(Cash a check or make a deposit but not both)

= [P(Cash a check) - P(Both)] + [P(Deposit) - P(Both)]

= (0.25 - 0.09) + (0.39 - 0.09)

= 0.16 + 0.30

= 0.46

e) P(Not cash a check) = 1 - 0.25 = 0.75

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