Sure, let's work through this step-by-step.
a) Chance of getting heads, tails, heads (HTH)
To determine the probability of getting the exact sequence "heads, tails, heads" when flipping a quarter three times, we need to consider the specific outcome out of all possible outcomes. Each of the three flips is an independent event with two possible outcomes: heads (H) or tails (T).
- The total number of possible outcomes when flipping a coin three times is [tex]\( 2^3 = 8 \)[/tex].
- The sequence "heads, tails, heads" (HTH) is only one of these 8 possible outcomes.
Therefore, the probability of getting the sequence HTH is:
[tex]\[ \frac{1}{8} = 0.125 \][/tex]
b) Chance of getting two heads in any order
We need to determine the probability of getting exactly two heads and one tail in any order from three flips. Let's identify all possible favorable outcomes:
- Possible sequences with two heads: HHT, HTH, and THH
So, there are 3 favorable outcomes.
- As mentioned before, the total number of possible outcomes is 8.
Therefore, the probability of getting two heads in any order is:
[tex]\[ \frac{3}{8} = 0.375 \][/tex]
c) Chance of getting tails all three times (TTT)
To find the probability of getting "tails, tails, tails" when flipping a coin three times:
- The sequence "tails, tails, tails" (TTT) is only one specific outcome out of the 8 possible outcomes.
So, the probability of getting TTT is again:
[tex]\[ \frac{1}{8} = 0.125 \][/tex]
To summarize:
a) The probability of getting heads, tails, heads (HTH) is [tex]\( 0.125 \)[/tex].
b) The probability of getting two heads in any order is [tex]\( 0.375 \)[/tex].
c) The probability of getting tails all three times (TTT) is [tex]\( 0.125 \)[/tex].
