There are 8 students. Each student has a fair quarter coin (that means the coin has two sides, head and tail, and the probability of getting a head is 0.5). Another student, whose name is Emily, asks the 8 students to flip their coins at the same time and counts the total number of heads she sees.
(1) What is the probability that Emily sees 3 heads?

a) 0.2188 b) 0.7812 c) 0.0039 d) 0.1250

(2) What is the probability that Emily sees 6 or less heads?

a) 0.8906 b) 0.0352 c) 0.1094 d) 0.9648

(3) What is the probability that Emily sees 6 or less tails?

a) 0.9648 b) 0.1445 c) 0.8555 d) 0.0352

(4) What is the probability that Emily sees between 2 (inclusive) and 6 (inclusive) heads?

a) 0.2734 b) 0.1797 c) 0.9298 d) 0.8203

1) Option A is correct.

P(X=3) = 0.2188

2) Option D is correct.

P(X ≤ 6) = 0.9648

3) Option A is correct.

P(X ≥ 2) = 0.9648

4) Option C is correct.

P(2 ≤ X ≤ 6) = 0.9298

Step-by-step explanation:

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 8 students with the coins

x = Number of successes required = variable

p = probability of success = probability of a head = 0.5

q = probability of failure = probability of a tail = 1 - 0.5 = 0.5

a) Probability that Emily sees exactly 3 heads

P(X=3)

x = 3

P(X=3) = ⁸C₃ (0.5)³ (0.5)⁸⁻³

P(X=3) = 0.21875 = 0.2188

2) Probability that Emily sees 6 or less heads

P(X ≤ 6)

P(X ≤ 6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

Solving each of these and adding the answers

P(X ≤ 6) = 0.96484375 = 0.9648

3) Probability that Emily sees 6 or less tails = Probability that Emily sees 2 or more heads

P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8)

Solving each of these and summing them all up

P(X ≥ 2) = 0.96484375 = 0.9648

4) Probability that Emily sees between 2 (inclusive) and 6 (inclusive) heads

P(2 ≤ X ≤ 6) = P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

Solving each of these and summing them all up

P(2 ≤ X ≤ 6) = 0.109375 + 0.21875 + 0.2734375 + 0.21875 + 0.109375 = 0.9296875 = 0.9297 ≈ 0.9298

Hope this Helps!!!

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have