A coin is tossed 6 times. Find the probability that all 6 tosses are tails.
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To find the probability of getting all tails in 6 coin tosses, we need to determine the probability of getting tails in a single toss.
Since there are two possible outcomes (heads or tails) for each coin toss, the probability of getting tails on a single toss is 1/2 or 0.5.
Since we want all 6 tosses to be tails, we need to multiply the probability of getting tails on each individual toss. Since the tosses are independent events, we can use the multiplication rule of probability.
So, the probability of getting all 6 coin tosses as tails is:
P(all tails) = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2)
Simplifying this expression, we get:
P(all tails) = (1/2)^6
Calculating this expression, we find:
P(all tails) = 1/64
Therefore, the probability of all 6 coin tosses being tails is 1/64 or approximately 0.0156.
To find the probability of all 6 tosses being tails, we need to determine the probability of getting a single tails on each individual toss and multiply them together.
When a fair coin is tossed, there are two possible outcomes: heads or tails. Since we want to find the probability of getting tails on each toss, we divide the number of favorable outcomes (i.e., all tails) by the total number of possible outcomes.
For a single coin toss, there are 2 possible outcomes (tails or heads), so the probability of getting tails on one toss is 1/2.
Since each toss is independent of the others, we can multiply the probabilities together to find the probability of getting tails on all 6 tosses:
Probability = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2)
To calculate this, we can multiply the fractions or raise 1/2 to the power of 6, which gives us:
Probability = (1/2)^6 = 1/64
Therefore, the probability of getting all 6 tosses as tails is 1/64.