GER1000 QUIZ 7
Please help to check: May not be entirely correct
1) A standard deck of playing cards consists of four suits: Spades, Hearts, Clubs and Diamonds. Each suit contains 13 cards: which are 2, 3, …, 10, Jack, Queen, King, Ace. So there are a total of 52 cards. A card is drawn at random, and you win $100 if it is a Heart or a King. What is the probability of winning $100?
ANS: 16/52
P(Heart) = 13/52 && P(King) = 4/52 && P(Heart AND King) = 1/52
THEREFORE, P(Heart or King) = P(Heart) + P(King) - P(Heart AND King) = 16/52
2) A particular insurance policy charges every subscriber a premium of $1,000. Suppose 0.2% of subscribers make claims of $100,000 each, and 1% of subscribers make claims of $10,000 each. The rest of the subscribers do not make any claims. What is the average gain of the insurance company per subscriber?
ANS: 700
Loss Per Customer = (0.2% * 100 000) + (1% * 10 000) = 300
Gain Per Customer = 1000 - 300 = 700
3) A standard deck of playing cards consists of four suits: Spades, Hearts, Clubs and Diamonds. Each suit contains 13 cards: which are 2, 3, …, 10, Jack, Queen, King, Ace. So there are a total of 52 cards. Which of the following pairs of events are independent?
ANS: Obtaining Heads on two tosses of a coin. P(Heads) = 1/2 always
Why not the other, probability changes when you remove a card from the deck.
P(King after 1st round if drawn King) = 3/51 != 4/52
P(King after 1st round if not drawn King) = 4/51 != 4/52
4) A device has two LED lights. When a button is pressed, the red light flashes with probability 0.6 and the blue light flashes with probability 0.6. The probability both lights will flash is 0.3. What is the probability that only the red light will flash?
ANS: 0.3
P(Red) = 0.6 && P(Blue) = 0.6 && P(Red AND Blue) = 0.3
P(Red OR BLUE) = 0.6 + 0.6 - 0.3 = 0.9
THEREFORE, P(Red ONLY) = P(Red OR Blue) - P(Blue) = 0.9 - 0.6 = 0.3
5) Three sensors, operating independently, are set to detect intruders moving through a certain area. Each sensor has a probability of 0.9 of detecting an intruder in this area. If an intruder enters the area, what is the probability it goes undetected?
ANS: 0.001
P(undetected) = 1 - P(detected) = 1 - 0.9 = 0.1
P(undetected 3 times) = P(undetected) ^ 3 = 0.1 * 0.1 * 0.1 = 0.001
Round 2
GER1000 QUIZ 7
Please help to check: May not be entirely correct
1) A standard deck of playing cards consists of four suits: Spades, Hearts, Clubs and Diamonds. Each suit contains 13 cards: which are 2, 3, …, 10, Jack, Queen, King, Ace. So there are a total of 52 cards. A card is drawn at random, and you win $100 if it is a Heart or a King. What is the probability of winning $100?
ANS: 16/52
P(Heart) = 13/52 && P(King) = 4/52 && P(Heart AND King) = 1/52
THEREFORE, P(Heart or King) = P(Heart) + P(King) - P(Heart AND King) = 16/52
2) A particular insurance policy charges every subscriber a premium of $1,000. Suppose 0.2% of subscribers make claims of $100,000 each, and 1% of subscribers make claims of $10,000 each. The rest of the subscribers do not make any claims. What is the average gain of the insurance company per subscriber?
ANS: 700
Loss Per Customer = (0.2% * 100 000) + (1% * 10 000) = 300
Gain Per Customer = 1000 - 300 = 700
3) A standard deck of playing cards consists of four suits: Spades, Hearts, Clubs and Diamonds. Each suit contains 13 cards: which are 2, 3, …, 10, Jack, Queen, King, Ace. So there are a total of 52 cards. Which of the following pairs of events are independent?
ANS: Obtaining Heads on two tosses of a coin. P(Heads) = 1/2 always
Why not the other, probability changes when you remove a card from the deck.
P(King after 1st round if drawn King) = 3/51 != 4/52
P(King after 1st round if not drawn King) = 4/51 != 4/52
4) A device has two LED lights. When a button is pressed, the red light flashes with probability 0.6 and the blue light flashes with probability 0.6. The probability both lights will flash is 0.3. What is the probability that only the red light will flash?
ANS: 0.3
P(Red) = 0.6 && P(Blue) = 0.6 && P(Red AND Blue) = 0.3
P(Red OR BLUE) = 0.6 + 0.6 - 0.3 = 0.9
THEREFORE, P(Red ONLY) = P(Red OR Blue) - P(Blue) = 0.9 - 0.6 = 0.3
5) Three sensors, operating independently, are set to detect intruders moving through a certain area. Each sensor has a probability of 0.9 of detecting an intruder in this area. If an intruder enters the area, what is the probability it goes undetected?
ANS: 0.001
P(undetected) = 1 - P(detected) = 1 - 0.9 = 0.1
P(undetected 3 times) = P(undetected) ^ 3 = 0.1 * 0.1 * 0.1 = 0.001
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