3. a toy factory produces model helicopters. in a quality control test of 675 helicopters, 8 were found to…

3. a toy factory produces model helicopters. in a quality control test of 675 helicopters, 8 were found to have broken propellers.\na) what is the probability that a model helicopter will have a broken propeller?\nb) if the factory produces 100 000 model helicopters, how many can be expected to have broken propellers?\n4. a) if a card is randomly chosen from a standard deck of playing cards, what is the theoretical probability that it will be an ace?\nb) zach wanted to compare the theoretical probability to the results of an experiment. he shuffled the deck of cards, chose the top card, and recorded the result. he did this 50 times. in the 50 trials, he picked up an ace twice. calculate the experimental probability of choosing an ace.\nc) how many times do you think an ace will be drawn in 2000 trials? explain your answer.

3. a toy factory produces model helicopters. in a quality control test of 675 helicopters, 8 were found to have broken propellers.\na) what is the probability that a model helicopter will have a broken propeller?\nb) if the factory produces 100 000 model helicopters, how many can be expected to have broken propellers?\n4. a) if a card is randomly chosen from a standard deck of playing cards, what is the theoretical probability that it will be an ace?\nb) zach wanted to compare the theoretical probability to the results of an experiment. he shuffled the deck of cards, chose the top card, and recorded the result. he did this 50 times. in the 50 trials, he picked up an ace twice. calculate the experimental probability of choosing an ace.\nc) how many times do you think an ace will be drawn in 2000 trials? explain your answer.

Answer

Explanation:

3.a)

Find probability ratio. $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{8}{675}$

3.b)

Use proportion to find expected value. Let $x$ be the expected number. Set up $\frac{8}{675}=\frac{x}{100000}$. Cross - multiply: $675x = 8\times100000$. Then $x=\frac{8\times100000}{675}=\frac{800000}{675}\approx1185.19\approx1185$

4.a)

Find theoretical probability for cards. A standard deck has 52 cards and 4 aces. So $P=\frac{4}{52}=\frac{1}{13}$

4.b)

Calculate experimental probability. $P=\frac{\text{Number of times an ace was picked}}{\text{Total number of trials}}=\frac{2}{50}=\frac{1}{25}$

4.c)

Use theoretical probability to predict. The theoretical probability of picking an ace is $\frac{1}{13}$. Let $y$ be the number of aces in 2000 trials. Set up proportion $\frac{1}{13}=\frac{y}{2000}$. Cross - multiply: $13y = 2000$. Then $y=\frac{2000}{13}\approx153.85\approx154$

Answer:

3.a) $\frac{8}{675}$ 3.b) 1185 4.a) $\frac{1}{13}$ 4.b) $\frac{1}{25}$ 4.c) 154