probability/grammar\ndetermine the probabilit...
probability/grammar\ndetermine the probability of each event.\n1 a tray has 16 doughnuts, 9 of which contain raspberry jam and 7 of which contain lemon curd. what is the probability that ling randomly selects a doughnut with raspberry jam and then alexander randomly selects a doughnut with lemon curd?\n2 marnie makes necklaces from beads of the same size and shape. she has a container of 30 beads, with an equal number of blue, red, and yellow beads. what is the probability that she randomly selects a blue bead, puts it back in the container, and then randomly selects a blue bead again?\n3 lamarcus flips a quarter and then flips a dime. what is the probability that both of the coins will land on heads?\n4 an art class has 18 students, including naoko and samir. the students write their names on slips of paper and place them into a hat. two slips will be selected from the hat without replacement. what is the probability that both naoko and samir will be selected?\nread the passage. draw a line under each word that should be capitalized.\n5 in 1775, the continental congress appointed the first postmaster general. the person was a historical figure who was familiar to most people: benjamin franklin. franklin helped to organize and develop the united states postal service, which is still in operation today, more than 200 years later. the first postage stamps were issued in 1847. in 1860, as the united states was expanding west, the pony express was born. over time, the u.s. postal service has continued to adapt, and letter carriers still work to deliver mail around the world today.
Answer
1.
# Explanation:
## Step1: Probability of Ling's selection
The probability that Ling selects a dough - nut with raspberry jam is the number of raspberry - jam doughnuts divided by the total number of doughnuts. There are 9 raspberry - jam doughnuts and 16 total doughnuts, so $P(\text{Ling})=\frac{9}{16}$.
## Step2: Probability of Alexander's selection
After Ling selects a doughnut, there are 15 doughnuts left. There are 7 lemon - curd doughnuts, so $P(\text{Alexander})=\frac{7}{15}$.
## Step3: Probability of both events
Since these are independent events (the first selection affects the second in terms of number of items left), the probability of both events is the product of their probabilities. $P = \frac{9}{16}\times\frac{7}{15}=\frac{9\times7}{16\times15}=\frac{63}{240}=\frac{21}{80}$.
# Answer:
$\frac{21}{80}$
2.
# Explanation:
## Step1: Probability of first blue - bead selection
There are 30 beads in total, and since there are an equal number of blue, red, and yellow beads, there are 10 blue beads. The probability of selecting a blue bead on the first draw is $P_1=\frac{10}{30}=\frac{1}{3}$.
## Step2: Probability of second blue - bead selection
Since the bead is put back, the total number of beads is still 30 and the number of blue beads is still 10. The probability of selecting a blue bead on the second draw is $P_2=\frac{10}{30}=\frac{1}{3}$.
## Step3: Probability of both events
Since the two draws are independent events (because of replacement), the probability of both events is the product of their probabilities. $P=\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}$.
# Answer:
$\frac{1}{9}$
3.
# Explanation:
## Step1: Probability of quarter landing on heads
The probability of a fair quarter landing on heads is $P(\text{quarter})=\frac{1}{2}$.
## Step2: Probability of dime landing on heads
The probability of a fair dime landing on heads is $P(\text{dime})=\frac{1}{2}$.
## Step3: Probability of both events
Since the flips of the quarter and the dime are independent events, the probability of both landing on heads is the product of their probabilities. $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.
# Answer:
$\frac{1}{4}$
4.
# Explanation:
## Step1: Probability of first selection
The probability that the first slip selected is either Naoko or Samir is $\frac{2}{18}$.
## Step2: Probability of second selection
After one of them is selected, there are 17 slips left and 1 of the remaining slips is the other one. So the probability that the second slip is the other person is $\frac{1}{17}$.
## Step3: Probability of both events
The probability of both events (selecting both Naoko and Samir) is the product of their probabilities. $P=\frac{2}{18}\times\frac{1}{17}=\frac{2}{306}=\frac{1}{153}$.
# Answer:
$\frac{1}{153}$
5.
# Explanation:
The words that should be capitalized are proper nouns and the first word of a sentence. "In 1775, the Continental Congress appointed the first Postmaster General. The person was a historical figure who was familiar to most people: Benjamin Franklin. Franklin helped to organize and develop the United States postal service, which is still in operation today, more than 200 years later. The first postage stamps were issued in 1847. In 1860, as the United States was expanding west, the Pony Express was born. Over time, the U.S. postal service has continued to adapt, and letter carriers still work to deliver mail around the world today."
# Answer:
In 1775, the Continental Congress appointed the first Postmaster General. The person was a historical figure who was familiar to most people: Benjamin Franklin. Franklin helped to organize and develop the United States postal service, which is still in operation today, more than 200 years later. The first postage stamps were issued in 1847. In 1860, as the United States was expanding west, the Pony Express was born. Over time, the U.S. postal service has continued to adapt, and letter carriers still work to deliver mail around the world today.