Let Y be a random number between 0 and 1 generated by an idealized random number generator. Find the following probabilities:

A. P (0 less than equal to Y less than equal to .6) =?

B. P (.3 less than equal to Y less than equal to .5) =?

C. P ( Y less than equal to .2 or .7 less than equal to Y) =?

PLEASE HELP!!! THANK YOU SOOOO MUCH! :)

an experiment consists of 4 tosses of a coin.denoting the outcomes HHTH,THTT,..and assuming that all 16 outcomes are equally likely, find the probability distribution for the total number of heads.

To find the probabilities in the given scenarios, we can use the properties of a uniform distribution. In a uniform distribution, the probability of any interval is proportional to the length of the interval.

A. P(0 ≤ Y ≤ 0.6):
In this case, we have a uniform distribution between 0 and 1. The length of the interval (0 to 0.6) is 0.6 - 0 = 0.6. Since the total length of the interval (0 to 1) is 1, the probability can be calculated as:
P(0 ≤ Y ≤ 0.6) = (0.6 - 0) / (1 - 0) = 0.6.

B. P(0.3 ≤ Y ≤ 0.5):
Again, we have a uniform distribution between 0 and 1. The length of the interval (0.3 to 0.5) is 0.5 - 0.3 = 0.2. Since the total length of the interval (0 to 1) is 1, the probability can be calculated as:
P(0.3 ≤ Y ≤ 0.5) = (0.5 - 0.3) / (1 - 0) = 0.2.

C. P(Y ≤ 0.2 or 0.7 ≤ Y):
To calculate this probability, we need to sum the individual probabilities of each interval. Since the intervals are mutually exclusive, we can add up the probabilities.
P(Y ≤ 0.2 or 0.7 ≤ Y) = P(Y ≤ 0.2) + P(0.7 ≤ Y).

For P(Y ≤ 0.2):
Using the same logic as in part A, the length of the interval (0 to 0.2) is 0.2 - 0 = 0.2. Since the total length of the interval (0 to 1) is 1, the probability can be calculated as:
P(Y ≤ 0.2) = (0.2 - 0) / (1 - 0) = 0.2.

For P(0.7 ≤ Y):
Similarly, the length of the interval (0.7 to 1) is 1 - 0.7 = 0.3. Since the total length of the interval (0 to 1) is 1, the probability can be calculated as:
P(0.7 ≤ Y) = (1 - 0.7) / (1 - 0) = 0.3.

Now, we can add up these individual probabilities:
P(Y ≤ 0.2 or 0.7 ≤ Y) = P(Y ≤ 0.2) + P(0.7 ≤ Y) = 0.2 + 0.3 = 0.5.

Therefore:
A. P(0 ≤ Y ≤ 0.6) = 0.6
B. P(0.3 ≤ Y ≤ 0.5) = 0.2
C. P(Y ≤ 0.2 or 0.7 ≤ Y) = 0.5.