4. Suppose that you buy a lottery ticket containing k distinct numbers from among {1,2,...,n} where 1 sk

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
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Indexing and Slicing - X
ments/a2/a2_2022.pdf
a2_2022.pdf
X
statistics - Probability x G A treasure chest cont. X
1/2 1
151% +
mr me card game pracK SUCK Your opponent
Gunt. At partourar, you can see your
au p
opponents face-up card. This lends itself to conditional probability. For each question specify events E₁ and E₂ so that the
give question is asking you to determine P(E₁ E2) and then answer the question.
(50) A treasure chest X +
I card and a face up cards
(a) What is the probability of that the face-down card is a 10, jack, queen or king, given that you see his face-up card is
an ace?
(b) What is the probability of that the face-down card is a 10, jack, queen or king, given that you see his face-up card is
an ace and you know your own hand consists of a 9 and a 10?
4. Suppose that you buy a lottery ticket containing k distinct numbers from among {1,2,..., n} where 1 <k<n. To determine
the winning ticket, k balls are randomly drawn without replacement from a bin containing n balls numbered 1, 2,..., n.
(a) What is the probability that at least one of the numbers on your lottery ticket is among those drawn from the bin?
(b) Prizes start when you have at least (ic. half) numbers in common with the drawn balls. Express the probability that
you win something. You may find it helpful to use summation notation.
5. The Toronto Blue Jays are going to the playoffs! Let's consider a best of three playoff series. If the Jays win every game
they play with probability, then what is the probability that the Jays will win their best of three series? A best of three
series means the first team to win 2 games wins the series.
6. A fair coin is tossed until either a head comes up or four tails are obtained. What is the expected number of tosses?
7. Suppose that a certain tech company sources their chips from three different factories, F1, F2 and F3. Suppose the percent-
ages of each shipment that are defective are 10%, 8% and 3% respectively. Factory F₁ supplies 20%, F2 supplies 30% and
F3 supplies 50% of the chips to the tech company. Suppose quality control selects a chip at random and it is defective. What
is the probability the chip came from factory F₂?
8. A treasure chest contains 25 gold coins and 15 silver coins. Two are chosen at random one after the other, without replace-
ment (ie, once you take the first one out, there are now 39 coins in the chest).
(a) Use a tree diagram to help calculate the following probabilities:
the probability that both coins are gold
• the probability that the first coin is gold and second is not
• the probability that the first coin is silver and the second is gold
1
4
Transcribed Image Text:Indexing and Slicing - X ments/a2/a2_2022.pdf a2_2022.pdf X statistics - Probability x G A treasure chest cont. X 1/2 1 151% + mr me card game pracK SUCK Your opponent Gunt. At partourar, you can see your au p opponents face-up card. This lends itself to conditional probability. For each question specify events E₁ and E₂ so that the give question is asking you to determine P(E₁ E2) and then answer the question. (50) A treasure chest X + I card and a face up cards (a) What is the probability of that the face-down card is a 10, jack, queen or king, given that you see his face-up card is an ace? (b) What is the probability of that the face-down card is a 10, jack, queen or king, given that you see his face-up card is an ace and you know your own hand consists of a 9 and a 10? 4. Suppose that you buy a lottery ticket containing k distinct numbers from among {1,2,..., n} where 1 <k<n. To determine the winning ticket, k balls are randomly drawn without replacement from a bin containing n balls numbered 1, 2,..., n. (a) What is the probability that at least one of the numbers on your lottery ticket is among those drawn from the bin? (b) Prizes start when you have at least (ic. half) numbers in common with the drawn balls. Express the probability that you win something. You may find it helpful to use summation notation. 5. The Toronto Blue Jays are going to the playoffs! Let's consider a best of three playoff series. If the Jays win every game they play with probability, then what is the probability that the Jays will win their best of three series? A best of three series means the first team to win 2 games wins the series. 6. A fair coin is tossed until either a head comes up or four tails are obtained. What is the expected number of tosses? 7. Suppose that a certain tech company sources their chips from three different factories, F1, F2 and F3. Suppose the percent- ages of each shipment that are defective are 10%, 8% and 3% respectively. Factory F₁ supplies 20%, F2 supplies 30% and F3 supplies 50% of the chips to the tech company. Suppose quality control selects a chip at random and it is defective. What is the probability the chip came from factory F₂? 8. A treasure chest contains 25 gold coins and 15 silver coins. Two are chosen at random one after the other, without replace- ment (ie, once you take the first one out, there are now 39 coins in the chest). (a) Use a tree diagram to help calculate the following probabilities: the probability that both coins are gold • the probability that the first coin is gold and second is not • the probability that the first coin is silver and the second is gold 1 4
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