1. An architect draws house plans for a client using the scale 1in= 4ft. How long shall the architect draw a wall that will be 22ft long
Ans 5 1/2 in
2. If a coin is flipped 5 times, the probability of getting heads all 5 times is
Ans 1/32
3. a bag of marbles contains 4 red, 3 blue, 2 yellow, and 1 green. If 2 marbles are drawn from the bag without replacement, the probability that both marbles are red is
Ans. 2/15
all correct
good work
1. Well, if you're building a house with walls that are only 5 1/2 inches tall, you might end up with a very cozy home for ants! But hey, who am I to judge your architectural choices?
2. Ah, the probability of flipping heads 5 times in a row? Well, let's just say your chances are about as likely as me becoming a world-class tightrope walker. In other words, it's pretty unlikely!
3. The probability of drawing two red marbles from that bag? It's like finding a needle in a haystack, only the needle is painted red and the haystack is filled with marbles of different colors. So, let's just say it's not the easiest task, but hey, anything is possible with a little bit of luck!
Sure! Here are step-by-step explanations for each question:
1. To find out how long the architect should draw a wall that will be 22ft long, you need to use the given scale of 1in = 4ft.
a. Divide the length of the actual wall (22ft) by the scale factor (4ft): 22ft / 4ft = 5.5.
b. This means that the architect should draw the wall as 5.5 inches long.
2. To calculate the probability of getting heads all 5 times when flipping a coin, you need to use the probability formula.
a. The probability of getting heads on a single flip of a fair coin is 1/2.
b. Since the coin is flipped 5 times, you multiply the individual probabilities together: (1/2)^5 = 1/32.
c. Therefore, the probability of getting heads all 5 times is 1/32.
3. To find out the probability of drawing two red marbles from a bag without replacement, you need to calculate the probability of each event and multiply them together.
a. Start with the total number of marbles in the bag, which is 10 (4 red + 3 blue + 2 yellow + 1 green).
b. The probability of drawing the first red marble is 4/10.
c. After drawing one red marble, the total number of marbles in the bag decreases to 9.
d. The probability of drawing the second red marble, without replacement, is 3/9.
e. Multiply the probabilities of drawing the first and second red marbles: (4/10) * (3/9) = 12/90.
f. Simplify the fraction: 12/90 = 2/15.
g. Therefore, the probability that both marbles drawn are red is 2/15.
I hope this helps! Let me know if you have any more questions.
To answer question 1:
The scale given is 1in=4ft. This means that for every 1 inch on the drawing, it represents 4 feet in reality.
To find out how long the architect should draw a wall that will be 22ft long, we can set up a proportion using the scale.
Let x represent the length in inches that the architect should draw. So we have the proportion:
1 inch / 4 feet = x inches / 22 feet
To solve for x, we can cross-multiply and then divide:
4 feet * x inches = 1 inch * 22 feet
4x = 22
x = 22/4
x = 5 1/2 inches
Therefore, the architect should draw a wall that is 5 1/2 inches long.
To answer question 2:
When flipping a fair coin, the probability of getting heads on any single flip is 1/2, since there are two equally likely outcomes: heads or tails.
To find the probability of getting heads on 5 consecutive flips, we can multiply the probabilities of each individual flip.
So, the probability of getting heads all 5 times is (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32.
Therefore, the probability of getting heads all 5 times is 1/32.
To answer question 3:
There are a total of 10 marbles in the bag. The probability of drawing the first red marble is 4/10, since there are 4 red marbles out of 10 total.
After removing one red marble from the bag, there are now 3 red marbles left out of 9 total. So the probability of drawing the second red marble is 3/9.
To find the probability of both marbles being red, we can multiply the probabilities of each draw.
So, the probability of both marbles being red is (4/10) * (3/9) = 12/90 = 2/15.
Therefore, the probability that both marbles drawn from the bag without replacement are red is 2/15.