High School Common Core Mathematics

Front 1

On April 15, 1912 the Titanic stuck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table.If one of the passengers is randomly selected, what is the probability that this passenger was in first class? Round your answer to three decimal places.

Back 1

P(passenger in 1st class)=324/1317= 0.246

Front 2

On April 15, 1912 the Titanic stuck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table. If one of the passengers is randomly selected, what is the probability that this passenger survived? Round your answer to three decimal places.

Back 2

P(passenger survived)=500/1317= 0.380

Front 3

On April 15, 1912 the Titanic stuck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table. If one of the passengers is randomly selected, what is the probability that this passenger was in first class and survived? Round your answer to three decimal places.

Back 3

P[(passenger was in first class) and (passenger survived)]=201/1317= 0.153

Front 4

On April 15, 1912 the Titanic stuck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table. If one of the passengers is randomly selected from the first class passengers, what is the probability that this passenger survived? Round your answer to three decimal places.

Back 4

P(passenger survived|passenger was in first class)= 201/324= 0.620

Front 5

On April 15, 1912 the Titanic stuck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table. If one of the passengers who survived is randomly selected, what is the probability that this passenger was in first class? Round your answer to three decimal places.

Back 5

P(passenger was in first class|passenger survived)=201/500=0.402

Front 6

On April 15, 1912 the Titanic stuck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table. If one of the passengers who survived is randomly selected, what is the probability that this passenger was in third class? Round your answer to three decimal places.

Back 6

P(passenger was in third class|passenger survived)=181/500=0.362

Front 7

On April 15, 1912 the Titanic stuck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table. Based on your calculations, why is the probability that one of the survivors was in first class larger than the probability that they were in third class.

Back 7

The probability that one of the surviving passengers was in first class is larger than the probability that they were in third class because there were more first class passengers that survived than there were third class passengers.

Front 8

One card is selected at random from the shown set of 6 cards, each of which has a number and a black or white symbol. Let B be the event that the selected card has a black symbol, and let F be the event that the selected card has a 5. Are the events B and F independent? Justify your answer with appropriate calculations.

Back 8

Out of the 6 cards, there are 3 with a black symbol, two with a 5, and only one card has a 5 and a black symbol. Therefore, P(B)=3/6=1/2 P(F)=2/6=1/3 P(B and F)=1/6 Since P(B)*P(F) = P(B and F), the two events B and F are independent.

Front 9

One card is selected at random from the shown set of 6 cards, each of which has a number and a black or white symbol. Let B be the event that the selected card has a black symbol, and let E be the event that the selected card has an 8. Are the events B and E independent? Justify your answer with appropriate calculations.

Back 9

Out of the 6 cards, there are 3 with a black symbols, and with with an 8, both of them with a black symbol. Therefore, P(B)= 3/6=1/2 P(E)= 2/6=1/3 P(B and E)= 2/6=1/3 Since P(B)*P(E) is not equal to P(B and E), the two events B and E are not independent.

Front 10

There are 4 red envelopes, 4 blue envelopes, and 4 $1 bills, which will be placed in 4 of the 8 envelopes. Define the event A as "you pick a lucky envelope (one that has a $1 in it)" and the event B as "you pick a blue envelope." Suppose one $1 bill is placed in a blue envelope, and the 3 remaining $1 bills are placed in 3 red envelopes. If you choose one envelope at random, what is the probability that you pick a lucky envelope? How would you write this probability symbolically (using letters A and/or B)?

Back 10

Out of 8 envelopes, 4 have $1 bills in them. So the probability of picking a lucky envelope is 4/8 = 1/2. Symbolically, P(A)= 1/2

Front 11

There are 4 red envelopes, 4 blue envelopes, and 4 $1 bills, which will be placed in 4 of the 8 envelopes. Define the event A as "you pick a lucky envelope (one that has a $1 in it)" and the event B as "you pick a blue envelope." Suppose one $1 bill is placed in a blue envelope, and the 3 remaining $1 bills are placed in 3 red envelopes. If you know that the envelope you picked is blue, what is the probability that you picked a lucky envelope? How would you write this probability symbolically (using letters A and/or B)? Does knowing that the envelope is blue change the probability of getting a lucky envelope?

Back 11

Out of 4 blue envelopes, only 1 has a $1 bill in it. So the probability of picking the lucky envelope is 1/4. Symbolically, P(A|B)= 1/4. This means that, yes, knowing the envelope picked was blue changed the probability.

Front 12

There are 4 red envelopes, 4 blue envelopes, and 4 $1 bills, which will be placed in 4 of the 8 envelopes. Define the event A as "you pick a lucky envelope (one that has a $1 in it)" and the event B as "you pick a blue envelope." Suppose 2 $1 bills are placed in red envelopes and the other 2 $1 bills are placed in blue envelopes. If you choose one evelope at random, what is the probability that you pick a lucky envelope? How would you write this probability symbolically (using letters A and/or B)?

Back 12

Out of 8 envelopes, 4 have $1 bills in them. So the probability of picking a lucky envelope is 4/8 = 1/2. Symbolically, P(A)= 1/2

Front 13

There are 4 red envelopes, 4 blue envelopes, and 4 $1 bills, which will be placed in 4 of the 8 envelopes. Define the event A as "you pick a lucky envelope (one that has a $1 in it)" and the event B as "you pick a blue envelope." Suppose 2 $1 bills are placed in red envelopes and the other 2 $1 bills are placed in blue envelopes. If you know that the envelope you picked is blue, what is the probability that you picked a lucky envelope? How would you write this probability symbolically (using letters A and/or B)? Does knowing that the envelope is blue change the probability of getting a lucky envelope?

Back 13

Out of 4 blue envelopes, two have $1 bills in them. So the probability of picking a lucky envelope is 2/4 = 1/2. Symbolically, P(A|B) = 1/2. This means that, in this case, knowing that the envelope was blue did not change the probability that the envelope was a lucky envelope.

Front 14

All of the upper-division students (juniors and seniors) at a high school were classified accroding to grade level and their response to the question, "How do you usually get to school?" The resulting data are summarized in the two-way table. If an upper-division student is selected at random, what is the probability that this student usually takes a bus to school?

Back 14

P(Bus)=180/546= 0.330

Front 15

All of the upper-division students (juniors and seniors) at a high school were classified accroding to grade level and their response to the question, "How do you usually get to school?" The resulting data are summarized in the two-way table. If a randomly selected upper-division student says that he or she is a junior, what is the probability that he or she usually walks to school?

Back 15

P(Walks|Junior)=56/274= 0.204

Front 16

Today there is a 55% chance of rain, a 20% chance of lightning, and a 15% chance of lighting and rain together. Are the two events "rain today" and "lightning today" independent events? Justify your answer.

Back 16

P(rain)=0.55 P(lightning)=0.2, p(lightning and rain)=0.15 P(lightning)*P(rain) =0.11 0.11 ≠ 0.15, so the two events are not independent.

Front 17

Today there is a 60% chance of rain, a 15% chance of lightning, and a 20% chance of lightning if it is raining. What is the chance of both rain and lightning today?

Back 17

P(lightning|rain)= P(lightning and rain)/P(rain) 0.2= P(lightning and rain)/ 0.6 P(lightning and rain)= 0.12 There is a 12% chance of both rain and lightning today.

Front 18

Today there is a 55% chance of rain, a 20% chance of lightning, and a 15% chance of lightning and rain. What is the chance that we will have rain or lightning today?

Back 18

P(lightning or rain) = P(lightning) + P(rain) - P(lightning and rain) P(lightning or rain) = 0.2+0.55-0.15 P(lightning or rain) = 0.6 There is a 60% chance of rain or lightning today

Front 19

Today there is a 50% chance of rain, a 60% chance of rain or lightning, and a 15% chance of rain and lightning. What is the chance that we will have lightning today?

Back 19

P(rain or lightning) = P(rain) + P(lightning) - P(rain and lightning) 0.6 = 0.5 + P(lightning) - 0.15 P(lightning)=0.25 There is a 25% of lightning today.