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# Probability Quiz

Wed 27 Jul, 2016 05:52 am
A senior lecturer is set to give a series of four lectures. If he doesnt give any one lecture, the lecture is given by his assistant. He is certain to give the first lecture. The probability of giving the second lecture is 0.45. If he gives the second lecture, the probability of giving the third is 0.7, otherwise it is 0.4. If he gives the third lecture, the probability of giving the fourth lecture is 0.35 otherwise it is 0.7. Calculate the probability that the lecture
1. gives all the four lectures
2. gives two lectures only
3. Gives lecture one and lecture four only
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Type: Question • Score: 1 • Views: 693 • Replies: 5
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mark noble

1
Wed 27 Jul, 2016 06:20 am
@hum,
engineer

2
Wed 27 Jul, 2016 06:42 am
@hum,
1. This requires a very specific order, yes to each lecture.
100% chance of one
45% chance of two
70% chance of three
35% chance of four
Multiply those together and you get 11%

3 (going out of order). Likewise, this requires a specific order of events
100% chance of one
55% chance of two (does not give the lecture)
60% chance of three (again, does not give the lecture)
70% chance of four
Multiple those and you get 23%

2: There are three ways to give two lectures, 1-2, 1-3 and 1-4. We've already calculated 1-4 above (which is why I went out of order.) Using the same technique:
1-2 = 100% x 45% x 30% x 30% = 4.1%
1-3 = 100% x 55% x 40% x 30% = 6.6%
All total you are looking at 34%

You should check these as I tossed them off quickly before work.
markr

1
Wed 27 Jul, 2016 06:22 pm
@engineer,
I think 1-3 should be .55 * .4 * .65 since he gave the third lecture (1-.35).
cicerone imposter

1
Wed 27 Jul, 2016 06:40 pm
@markr,
Gosh, I wish I remembered my Statistics class, but that was over 50 years ago.
I can barely remember something about the bell curve.
Like they say, use it or lose it. I lost it.
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mark noble

1
Thu 28 Jul, 2016 07:37 am
@mark noble,
Not knowing what the lecture is about negates the question.
Anyone who 'plays-along' with this question, and tries to answer it - Is worthy of sympathy.
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