23 Jun A society has as members 20 women, 18 men, and 30 children.
A society has as members 20 women, 18 men, and 30 children.
a) How many ways are there to select a committee of 3 women, 2 men, and 1 child?
5232600
b) How many ways are there to select a committee of 6 members if the only restriction is that there be at least 1 woman on the committee?
97181832
c) How many ways are there to select a committee of 6 members if the only restriction is that there be at least 1 woman and at least 1 man on the committee?
81884907
2. The probability of success for a given experiment is 0.36 (every time)
a) If there are twelve trials, what is the probability that the number of successes will be within one standard deviation of the expected number of successes ?
E(X) = 4.32 ?(X) = 1.66… P(3) + P(4) + P(5) = 0.63
b) What is the probability that the fifth success will occur before the ninth trial ? (try lateral thinking)
0.118
3. A new configuration of the computer key board has 10 of the 26 letters
of the alphabet in different positions from the standard keyboard, and
the rest are in the usual places. If a perfectly accurate touch typist types the word computer on the new keyboard without looking, what is the probability that there will be at least two mistakes in the resulting printed word ? It may be assumed that the typist does not know the new configuration.
Hypergeometric 0.9185
4. The probability of success for a given experiment is 0.6 (every time)
a) If there are twelve trials, what is the probability that there will be more than the mean number of successes ?
0.438
b) What is the probability that the fifth success will occur on either the tenth or eleventh trial ? (hard)
0.1672
5. In a group of 1875 scientists, 900 were educated in Canada, and the rest were educated elsewhere. Only 75 of the scientists were educated in Eurelia. A random selection was made of eight of the scientists.
a) What is the exact probability that at most four of them were educated in Canada ? Use an approximate distribution to get an approximation to the exact answer as well.
Exact (hypergeometric) 0.679883632….
Approximation (binomial) 0.6795
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