Independent Events
Kelvin and Cynthia are
the ones in charge of washing dishes from Monday to Friday. The tree diagram
list the possible outcomes of Kelvin or Cynthia washing dishes from Monday to
Friday. The probability of Kelvin washes dishes is 11 out of 20.
Cynthia washes dishes
9 out of 20. Because Kelvin washes dishes the most, he complains to our parents
that Cynthia doesn’t wash the dishes. He calculates for our parents what the
probability of Cynthia washing dishes at least three of the five days is.
Answer: It is an
independent event because the probability of an event occurring is not affected
by an event that has occurred. The probability of Kelvin and Cynthia washing dishes on a given night is fixed. Therefore, we multiply the probabilities of the five nights to determine the probability of each outcome.
A = Cynthia Washing dishes
P (A>_3) = KKCCC + KCKCC + KCCKC + KCCCK + KCCCC + CKKCC + CKCKC + CKCCK + CKCCC + CCKKC + CCKCK + CCKCC + CCCKK + CCCKC + CCCCK + CCCCC
= 0.0276 + 0.0276 + 0.0276 + 0.0276 + 0.0226 + 0.0276 + 0.0276 + 0.0276 + 0.0226 +
0.0276 + 0.0276 +0.0226+ 0.0276 + 0.0226 + 0.0226 + 0.0184
= 0.4074 / 40.74%
∴ The probability that Cynthia washes dishes for three or more days in a week is 40.74%.
∴ Kelvin is correct that he washes more dishes than Cynthia.
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