Chapter 2: Q11SE (page 91)
Suppose that there is a probability of\(\frac{1}{{50}}\)that you will win a certain game. If you play the game 50 times, independently, what is the probability that you will win at least once?
Probability that someone will win at least once is \(1 - {\left( {\frac{{49}}{{50}}} \right)^{50}}\).
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Suppose that in 10 rolls of a balanced die, the number 6 appeared exactly three times. What is the probability that the first three rolls each yielded the number 6?
If A⊂B with Pr(B) > 0, what is the value of \({\bf{Pr}}\left( {{\bf{A}}|{\bf{B}}} \right)\) ?
Use the prior probabilities in Example 2.3.8 for the events\({B_1},...,{{\bf{B}}_{11}}\). Let \({E_1}\)be the event that the first patient is a success. Compute the probability of \({E_1}\) and explain why it is so much less than the value computed in Example 2.3.7.
Suppose that 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think that it is defective and remove it from the filling line.
a. If a bottle is removed from the filling line, what is the probability that it is defective?
b. If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective?
The probability that any child in a certain family will have blue eyes is 1/4, and this feature is inherited independently by different children in the family. If there are five children in the family and it is known that at least one of these children has blue eyes, what is the probability that at least three of the children have blue eyes?
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