Algebra
Probability

# When tossing 5 coins simultaneously what is the probability one will land heads up?

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The probability that exactly one will land heads up is 0.15625

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## Related Questions Probability of no heads = (0.5)^5 = 0.03125Probability of at least one head = 1 - probability of no heads = 1 - 0.03125 = 0.96875       The probability would be once in 128 attempts. You don't have to toss seven coins simultaneously. the 7 tosses just have to be independent of one another. No matter how many coins are thrown, the possibility of having AT LEAST ONE 'head' is 50%. This changes if you specify the number of 'heads' that must be shown. The probability of tossing a coin and getting heads is 0.5  This is easiest to solve by working out the probability that no heads show and subtracting this from 1 to give the probability that at least one head shows: Assuming unbiased coins which won't land and stay on their edge, the probability of head = probability of tail = &frac12; &rarr; probability no heads = probability 5 tails = &frac12;^5 = 1/32 &rarr; probability of at least one head = 1 - 1/32 = 31/32 = 0.96875 = 96.875 % = 96 7/8 % The probability of tossing 6 heads in 6 dice is 1 in 26, or 1 in 64, or 0.015625. THe probability of doing that at least once in six trials, then, is 6 in 26, or 6 in 64, or 3 in 32, or 0.09375. The probability of tossing heads on all of the first six tosses of a fair coin is 0.56, or 0.015625. The probability of tossing heads on at least one of the first six tosses of a fair coin is 1 - 0.56, or 0.984375. The probability of something NOT happening is the complement of the probability of something happening. Since the probability that you DO have 3 heads is 1/8 (that is, 1/2 cubed), the complement is 1 - 1/8 = 7/8.  There are 8 permutations of three coins. Of these, 3 of them have two heads, so the probability of tossing two heads on three coins is 3 in 8, or 0.375. However, you said, "at least", so that includes the case of three heads, so the probability of throwing at least two heads is 4 in 8, or 0.5. T T T T T H T H T T H H * H T T H T H * H H T * H H H * The probability that both coins are heads is the probability of one coin landing heads multiplied by the probability of the second coin landing heads: (.5) * (.5) = .25 or (1/2) * (1/2) = 1/4 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. 3 coins can land in 8 different ways. Only one of these ways is all tails. So the probability of rolling at least one heads is 7/8 = 87.5% . Potentially inclusive events are events that can happen simultaneously. For example, events A and B can occur at the same time. When these events do cannot occur simultaneously, then then are called Mutually exclusive (opposite). Potentially Inclusive: If A is heads of Coin 1 and B is heads of Coin 2, then tossing of both the coins is potentially inclusive since you can get heads on both the coins same time. Mutually exclusive: If A is heads and B is tails , then tossing of a coin is mutually exclusive since you cannot get heads and tails at the same time. You either get heads or tails. Looking at the total possibilities, you have eight different outcomes: TTT TTH THH HHH HHT HTT HTH THT Counting your two heads, one tails, you get a total of 3 possibilities out of 8, or 3/7  The probability of getting only one tails is (1/2)7. With seven permutations of which flip is the tails, this gives a probability of: P(six heads in seven flips) = 7*(1/2)7 = 7/128 1/2 * 1/2 = 1/4 1/2= probability of landing an even number 1/2 = probability of landing a heads

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