Three fair coins are tossed. What is the probability that at least one is a head? (Enter the probability as a fraction.) I came up with 7/8
Thank you
find probability that NONE are heads
(1/2)^3 = 1/8
so we want
1 - 1/8 = 7/8 agree with you
To find the probability that at least one coin is a head when three fair coins are tossed, we can use the concept of complementary events.
The complementary event to the event "at least one coin is a head" is "no coin is a head." Therefore, we can find the probability of this complementary event and subtract it from 1 to get the probability of the original event.
When no coin is a head, it means all three coins are tails. Since each coin has a 1/2 probability of landing on tails, the probability of all three coins landing on tails is (1/2) * (1/2) * (1/2) = 1/8.
Therefore, the probability of at least one coin being a head is 1 - 1/8 = 7/8.
So, your answer of 7/8 is correct.
To calculate the probability that at least one coin is a head, you can use the concept of complementary probability. The complementary event to "at least one head" is "no heads." In other words, if we find the probability of getting no heads and subtract it from 1, we will get the probability of getting at least one head.
To get the probability of getting no heads, we consider that each coin has two possible outcomes: heads or tails. Since all three coins are fair, the probability of getting tails on any individual coin is 1/2. To find the probability of getting no heads with all three coins, we can multiply these probabilities together.
Probability of getting tails on the first coin: 1/2
Probability of getting tails on the second coin: 1/2
Probability of getting tails on the third coin: 1/2
Now, we multiply these probabilities together:
(1/2) * (1/2) * (1/2) = 1/8
So, the probability of getting no heads is 1/8.
Since the probability of getting at least one head is the complement of getting no heads, we subtract the probability of getting no heads from 1:
1 - 1/8 = 7/8
Therefore, the correct probability of getting at least one head when tossing three fair coins is indeed 7/8. Well done!