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The total number of outcomes is 2^5 = 32.
If you toss eight coins, there are 256 (28) different outcomes.
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.
1 in 4
The odds are 1 in 2.
16
There are 210 = 1024 of them.
There are 2^10 = 1024 of them.
When flipping a coin, there are 2 possible outcomes. When flipping 3 coins there are 8 possible outcomes (2^3=8). As for the situation described, there is only one way for it to not be true, if all the coins land on the same side. So either all heads or all tails. This leaves 8-2=6 possible outcomes resulting in the above situation. Therefore the probability of the given situation is 6/8 or 3/4=75%
75% is not correct. The odds of flipping 4 independent coins is the same as flipping one coin 4 times. The number of outcomes of 4 flips is 2^4 or 16. The number of ways to exactly get 3 Heads is 4 (THHH, HTHH, HHTH, HHHT) so your chance of flipping 3 heas is 4/16 or 25%. If you include the occurance that produced 4 of 4 Heads, then you get 5/16 or 31.25%.
The total number of outcomes is 2^5 = 32.
Because the theory of coin flipping is well understood and so theoretical probabilities can be used.
The probability of flipping three heads when flipping three coins is 1 in 8, or 0.125. It does not matter if the coins are flipped sequentially or simultaneously, because they are independent events.
Only if you're counting order. If you call a head then a tail different from a tail and then a head then there are 8 outcomes from the coins; otherwise there are only 4. And clearly a number cube can have anywhere from 1 to 6 outcomes, depending on whether the same number appears multiple times.
Assuming the coins are fair, two-sided coins, and landing on their sides is not an option, there are four possible outcomes if you consider coin a having a head and coin b having a tail being a different instance from coin a being a tail and coin be having a head. Here they are; Coin A | Coin B Heads | Tails Heads | Heads Tails....| Heads Tails....| Tails
The probabilty of you flipping 3 coins and getting all heads or tails is 0.125 or 1/8.
The probability of flipping three tails with three coins is (1 in 2)3 or 1 in 8 or 0.125.