No.
The number of outcomes is 24 which is 16, not 64.
Furthermore, probability is a number that is associated with an outcome and is a number in the range [0, 1]. Neither 16 nor 64 are number in the relevant range.
Because there are only 2 outcomes for the flip of a coin, for 5 flips you just need to take (1/2)5, which equals 1/32. This implies there are 32 different outcomes for the case of tossing a coin 5 times. From these 32 outcomes 5 have exactly 4 heads: THHHH, HTHHH, HHTHH, HHHTH, and HHHHT. So the probability of getting exactly 4 heads when you toss a coin 5 times is: P(4H,!T) = 5/32 = 0.15625 ≈ 15.6%
a and b both have the probability of 3/4
The probability is 0.664
On a standard pair of six-sided dice, there are two ways to roll a "3"; i.e., a "1" and a "2" or a "2" and a "1". There are 36 possible outcomes. Therefore, the probability of rolling exactly 3 is 2/36, which equals 1/18. The probability of rolling 3 or higher is 35/36. The probability of rolling 3 or lower is 3/36, which is 1/12.
Impossible
Probability equals favorable outcomes divided by total number of outcomes.
Because there are only 2 outcomes for the flip of a coin, for 5 flips you just need to take (1/2)5, which equals 1/32. This implies there are 32 different outcomes for the case of tossing a coin 5 times. From these 32 outcomes 5 have exactly 4 heads: THHHH, HTHHH, HHTHH, HHHTH, and HHHHT. So the probability of getting exactly 4 heads when you toss a coin 5 times is: P(4H,!T) = 5/32 = 0.15625 ≈ 15.6%
When considering the probability of two different events or outcomes, it is essential to clarify whether they are mutually exclusive or independent. If the events are mutually exclusive, then the probability that either one or the other will occur equals the sum of their individual probabilities. This is known as the law of addition. If, however, two or more events or outcomes are independent, then the probability that both the first and the second will occur equals the product of their individual probabilities. This is known as the law of multiplication.
Each coin toss is a Bernoulli trial with a probability of success of .5. The probability of tossing heads exactly 3 times out of five is3 ~ Bin(5, 1/2), which equals(5!/(3!(5-3)!))(0.5^3)(1-0.5)^(5-3), which is 0.3125.
a and b both have the probability of 3/4
The probability that an event will occur plus the probability that it will not occur equals 1.
It does not matter.
The probability is 0.664
There are 5 letters in the set {a, b, c, d, e}, and 2 of these letters are vowels (a, e). Therefore, the probability of randomly choosing a vowel from this set is the number of favorable outcomes (2 vowels) divided by the total number of possible outcomes (5 letters), which equals 2/5 or 0.4.
On a standard pair of six-sided dice, there are two ways to roll a "3"; i.e., a "1" and a "2" or a "2" and a "1". There are 36 possible outcomes. Therefore, the probability of rolling exactly 3 is 2/36, which equals 1/18. The probability of rolling 3 or higher is 35/36. The probability of rolling 3 or lower is 3/36, which is 1/12.
Impossible
The answer depends on what the distribution is!