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.

To answer these questions, we need to use the given information and apply relevant mathematical concepts. Let's go through each question step by step:

1. To find the length the architect should draw for a wall that is 22ft long, we need to use the given scale of 1in = 4ft.

First, we convert the length of the wall from feet to inches: 22ft * 12in/ft = 264in.

Then, we divide the length in inches by the scale to find the corresponding length on the drawing: 264in / 4ft = 66in.

Therefore, the architect should draw a wall that is 66 inches long.

To find the answer in feet and inches, divide the length in inches by 12 to get the whole number of feet. The remainder will be the number of inches. In this case, 66 inches is equal to 5 feet and 6 inches, or 5 1/2 inches.

2. To find the probability of getting heads all 5 times when a coin is flipped, we need to use the concept of probability.

The probability of getting heads on a single coin flip is 1/2, as there are two possible outcomes: heads or tails.

Since the coin is flipped 5 times and each flip is independent, we can multiply the probabilities of each individual flip.

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.

3. To find the probability of drawing two red marbles from a bag without replacement, we need to use the concept of conditional probability.

First, we calculate the total number of marbles in the bag: 4 red + 3 blue + 2 yellow + 1 green = 10 marbles.

Since we are drawing 2 marbles without replacement, the total number of possibilities is reduced by 1 after each draw.

For the first draw, there are 10 marbles to choose from, with 4 red marbles.

After the first draw, for the second draw, there are remaining 9 marbles, with 3 red marbles.

To find the probability of drawing both marbles red, we multiply the probabilities of each draw.

The probability of drawing a red marble on the first draw is 4/10.

The probability of drawing a red marble on the second draw after a red one has been chosen is 3/9.

Therefore, the probability of drawing two red marbles is (4/10) * (3/9) = 12/90.

Simplifying the fraction, we get 2/15.

Therefore, the probability that both marbles drawn are red is 2/15.