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Probability Review
1.
If a coin is tossed twice, what is the probability that it will land on "tails" both times?
1 x 1 = 1 2 2 4 If two coins are tossed simultaneously, what is the probability they will both show "tails"? Possible outcomes (H,H) (H,T) 1 (T,H) (T,T) 4
2.
Find the probability of getting a face card or a heart on a single cut of a deck of cards. P(F or H) = P(F) + P(H) P(F and H)
= 12 + 13 3 52 52 52 = 22 11 = 52 26
3.
Find the probability of getting a face card or a heart on a single cut of a deck of cards. Yicong
4.
Four cards are dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly two face cards. sample space = 52C4 face cards = J, Q, K so 3 x 4 = 12 =
12C2 other 2 cards = 40C2 12C2 . 40C2 P (2 face) = = 0.19 52C4
5.
A committee of five shareholders is to be chosen by lot from seven men and five women. What is the probability that the committee will consist of three men and two women? sample space = 12C5
success = 7C3 x 5C2 7C3 x 5C2 = 175 probability = 12C5 396
6.
A test for Type 2 diabetes measures the blood glucose level after eight hours of fasting. Consider a blood glucose level above normal to be a positive result and anything else to be a negative result. This test is 85% accurate, and 2% of the world's population actually has diabetes. Determine P(diabetic tests positive) hint: draw a tree diagram 0.1037 or 10.3%
7.
8.
Polygraph or lie detector test are generally not very accurate. Suppose a polygraph is 70% accurate. Assuming that the average person is truthful 90% of the time. Determine the probability that a person is telling the truth, given that the polygraph test indicates truth.
0.954 or 95.4%
9.
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