A coin is tossed 9 times.
What is the probability of getting all heads? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
p(heads) = 1/2 on each throw.
So, p(9 heads) = (1/2)^9 = 1/512
Well, getting all heads in 9 coin tosses can be quite a rare occurrence. It's like finding a unicorn wearing a top hat and riding a unicycle while juggling flaming torches. Quite improbable, but let's crunch the numbers nonetheless.
Each coin toss has two possible outcomes: heads or tails. So for each individual toss, the probability of getting heads is 1/2. Since we're tossing the coin 9 times, we multiply these probabilities together:
(1/2)^(9) = 1/512 or approximately 0.00195
So, the probability of getting all heads in 9 coin tosses is 1/512 or 0.00195 if you're into decimals. But hey, don't let that stop you from chasing unicorns and improbable dreams!
A coin is tossed 6 times.
What is the probability of getting all tails? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
p(tails) = 1/2 on each throw.
So, p(6 tails) = (1/2)^6 = 1/64.
Answer: 1/64 or 0.0156
To calculate the probability of getting all heads when a coin is tossed 9 times, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Each coin toss has two possible outcomes: heads (H) or tails (T). Since there are 2 possible outcomes for each toss, the total number of possible outcomes for 9 tosses is 2^9 = 512.
To get all heads, there is only one favorable outcome where all the tosses result in heads. Therefore, the number of favorable outcomes is 1.
The probability of getting all heads is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 1 / 512 = 0.001953125
Rounded to four decimal places, the probability of getting all heads is approximately 0.0019.
Thus, the probability of getting all heads when a coin is tossed 9 times is 0.0019 or approximately 0.19%.