A survey from sigma research found out that 30% of IUCG students receive their spending money at the beginning of the academic session.if five students are selected at random,find the probability that at least three of them received their spending money at the beginning of the session.

Which of the following are binomial experiments or can be reduced to binomial experiments?
I.surveying 100 aspiring students to determine if they are interested in pursuing their tertiary education at IUCG.
ii.tossing a coin a 100 times to see how many heads occur.
III.Testing four different cars to see which brands are effective.
iv.Asking 100 people if they drink alcohol.
v.Testing a brand of car using 100 people to determine whether it is effective.

To find the probability that at least three students received their spending money at the beginning of the session, we need to consider the different possible outcomes.

Let's use the binomial probability formula to calculate the probability.

The formula for the probability of having exactly k successes in n trials, where the probability of success in a single trial is p, is:

P(X = k) = nCk * p^k * (1-p)^(n-k)

In this case:
n = 5 (number of students selected)
k = 3, 4, or 5 (at least three students received money at the beginning of the session)
p = 0.30 (probability of a student receiving money at the beginning of the session)

We need to calculate the probability for k = 3, 4, and 5, and then sum them to find the total probability of at least three students receiving money at the beginning of the session.

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)

P(X = 3) = 5C3 * (0.30)^3 * (1-0.30)^(5-3)
P(X = 4) = 5C4 * (0.30)^4 * (1-0.30)^(5-4)
P(X = 5) = 5C5 * (0.30)^5 * (1-0.30)^(5-5)

Calculating these probabilities:

P(X = 3) = 10 * (0.30)^3 * (0.70)^2
P(X = 4) = 5 * (0.30)^4 * (0.70)^1
P(X = 5) = 1 * (0.30)^5 * (0.70)^0

Now, we can sum these probabilities to find the total probability of at least three students receiving money at the beginning of the session:

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)

= (10 * (0.30)^3 * (0.70)^2) + (5 * (0.30)^4 * (0.70)^1) + (1 * (0.30)^5 * (0.70)^0)

= 0.1323 + 0.0283 + 0.0024

= 0.163

Therefore, the probability that at least three students received their spending money at the beginning of the session is 0.163.

Regarding the list of experiments:

i. Surveying 100 aspiring students to determine if they are interested in pursuing their tertiary education at IUCG.
This is not a binomial experiment since it has only one trial and there is no fixed probability of success for each trial.

ii. Tossing a coin 100 times to see how many heads occur.
This is a binomial experiment as it has a fixed number of trials (100) and each trial has a fixed probability of success (0.5 for heads).

III. Testing four different cars to see which brands are effective.
This is not a binomial experiment since it involves testing multiple different cars instead of a fixed number of trials with a fixed probability of success.

iv. Asking 100 people if they drink alcohol.
This is not a binomial experiment since it has only one trial and there is no fixed probability of success for each trial.

v. Testing a brand of car using 100 people to determine whether it is effective.
This is not a binomial experiment since it involves testing multiple people instead of a fixed number of trials with a fixed probability of success.

To find the probability that at least three out of five students received their spending money at the beginning of the session, we need to calculate the probability of three, four, and five students receiving their spending money and then add them together.

First, let's calculate the probability of exactly three students receiving their spending money:
P(3 students receiving money) = C(5, 3) * (0.3)^3 * (0.7)^2, where C(5, 3) is the combination formula for choosing 3 students out of 5.

Next, let's calculate the probability of exactly four students receiving their spending money:
P(4 students receiving money) = C(5, 4) * (0.3)^4 * (0.7)^1, where C(5, 4) is the combination formula for choosing 4 students out of 5.

Finally, let's calculate the probability of all five students receiving their spending money:
P(5 students receiving money) = C(5, 5) * (0.3)^5 * (0.7)^0, where C(5, 5) is the combination formula for choosing 5 students out of 5.

The probability of at least three students receiving their spending money is the sum of these three probabilities:
P(at least 3 students receiving money) = P(3 students receiving money) + P(4 students receiving money) + P(5 students receiving money).

Now let's consider which of the given scenarios can be considered binomial experiments or can be reduced to binomial experiments:

i. Surveying 100 aspiring students to determine if they are interested in pursuing their tertiary education at IUCG.
This scenario can be considered as a binomial experiment. Each student is independent, and the probability of each student being interested can be assumed to be constant.

ii. Tossing a coin 100 times to see how many heads occur.
This scenario is a binomial experiment. Each coin toss is independent, and the probability of getting heads (or tails) is constant.

iii. Testing four different cars to see which brands are effective.
This scenario is not a binomial experiment. It involves testing multiple cars, which can have different outcomes and probabilities. It cannot be reduced to a simple binomial experiment.

iv. Asking 100 people if they drink alcohol.
This scenario could be considered as a binomial experiment if the question is answered with a yes or no and the probability of each person saying yes is constant.

v. Testing a brand of car using 100 people to determine whether it is effective.
This scenario is not a binomial experiment. It involves testing a brand of car on multiple people, which can have different outcomes and probabilities. It cannot be reduced to a simple binomial experiment.