Probability of At Least One Head in Three Coin Tosses
This solution calculates the probability of obtaining at least one head when tossing three coins simultaneously.
Total Possible Outcomes
Each coin toss has two possible outcomes: Heads (H) or Tails (T). When tossing three coins, the total number of possible outcomes is calculated as:
Total Outcomes = $2^n$, where $n$ is the number of coins.
In this case, $n=3$, so the total number of outcomes is $2^3 = 8$. These outcomes are: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Calculating Probability Using the Complement
It's often easier to calculate the probability of the event *not* happening and subtract it from 1. The complement of getting "at least one head" is getting "no heads" at all.
Complementary Event: No Heads
The only outcome with no heads is getting all tails (TTT).
Probability of the Complementary Event
The probability of getting tails on a single fair coin toss is $\frac{1}{2}$. Since the tosses are independent, the probability of getting three tails (TTT) is:
$P(\text{No Heads}) = P(\text{TTT}) = P(T) \times P(T) \times P(T) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$
Probability of At Least One Head
The probability of the event we are interested in (at least one head) is 1 minus the probability of its complement (no heads):
$P(\text{At least one head}) = 1 - P(\text{No Heads})$
$P(\text{At least one head}) = 1 - \frac{1}{8} = \frac{8}{8} - \frac{1}{8} = \frac{7}{8}$
Conclusion
The probability of getting at least one head when tossing three coins is $\frac{7}{8}$.
Similar Questions
- A bowl contains 9 blue balls, 7 white and 5 black balls. If 2 balls are drawn in one go, then the probability of exactly one ball being white is:
- If 9 students are standing on a circular path, then the probability that 2 of them are always standing together is:
- A letter of English alphabet is chosen at random. Probability of getting a vowel is:
- Five salesmen, A, B, C, D and E, of a company are considered for a three member trade delegation to represent the company at an international trade conference. What is the probability that A gets selected?
- A dice is thrown twice and the sum of the appearing numbers is 10. Then the probability that the number 5 has appeared at least once is:
- A box contains 2 black, 6 green and 4 yellow balls. If 2 balls are picked up at random, the probability that both are green-coloured is:
- A bag contains cards numbered between 33 and 92. If one card is drawn from the bag, the probability that the number on the drawn card is a perfect square is:
- Kings and Queens of black colour are taken out from a deck of 52 playing cards. A card is drawn from the remaining well-shuffled cards. Probability of getting a spade card is:
- A card is drawn at random from a pack of playing cards. What is the probability of getting a face card?
- If we select 3 persons randomly from a group, consisting of 4 men, 3 women and 2 boys, then the probability that 2 men are selected is:
Important Questions from Probability
The probability of being 53 Sundays in year 2020 is-
Three dice are thrown randomly. The probability of coming 3 in at least one die is
The probability of having 53 Tuesdays in an ordinary year is:
When two dice are tossed simultaneously, the probability that the sum of the numbers appearing on both the dice is 8 will be
How many 3 - digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
