Question:
A coin is tossed three times. The probability of getting at least two heads is:
A coin is tossed three times. The probability of getting at least two heads is:
Show Hint
To find the probability of at least two heads, calculate the sum of probabilities for exactly two and three heads using the binomial formula, or use the complement rule.
Updated On: Jul 17, 2025
- \(\frac{1}{2}\)
- \(\frac{3}{8}\)
- \(\frac{1}{8}\)
- \(\frac{1}{4}\)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
When a coin is tossed three times, the total number of possible outcomes is \(2^3 = 8\) (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT).
The favorable outcomes for getting at least two heads are those with exactly two heads or three heads:
- Exactly two heads: HHT, HTH, THH (3 outcomes)
- Three heads: HHH (1 outcome)
Total favorable outcomes = \(3 + 1 = 4\).
The probability is the number of favorable outcomes divided by the total number of outcomes:
\[
\text{Probability} = \frac{4}{8} = \frac{1}{2}
\]
Was this answer helpful?
0
0
Top Questions on Probability
- If $P(A) = \frac{1}{7}$, $P(B) = \frac{5}{7}$ and $P(A \cap B) = \frac{4}{7}$, then $P(A | B)$ is:
- If $ A $ and $ B $ are two events such that $ P(A) = 0.7 $, $ P(B) = 0.4 $ and $ P\left( A \cap \overline{B} \right) = 0.5 $, where $\overline{B}$ denotes the complement of $ B $, then $ P\left( B | \left( A \cup \overline{B} \right) \right) $ is equal to
- JEE Main - 2025
- Mathematics
- Probability
- If the probability that the random variable X takes the value x is given by \( P(X = x) = k(x + 1)3^{-x} \), \( x = 0, 1, 2, 3, ... \), where k is a constant, then \( P(X \ge 3) \) is equal to
- JEE Main - 2025
- Mathematics
- Probability
- All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $ n $ be denoted by $ W_n $. Let the probability $ P(W_n) $ of choosing the word $ W_n $ satisfy $ P(W_n) = 2P(W_{n-1}) $, $ n>1 $. If $ P(CDBEA) = \frac{2^\alpha}{2^\beta - 1} $, $ \alpha, \beta \in \mathbb{N} $, then $ \alpha + \beta $ is equal to :
- JEE Main - 2025
- Mathematics
- Probability
- A coin is tossed and a card is selected at random from a well shuffled pack of 52 playing cards. The probability of getting head on the coin and a face card from the pack is:
View More Questions
Questions Asked in CBSE CLASS XII exam
- A ladder 13 m long is leaning against the wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 2 m/s. How fast is the height on the wall decreasing when the foot of the ladder is 12 m away from the wall?
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Application of derivatives
- Write the reactions involved in the following:
- CBSE Compartment XII - 2025
- Organic Reactions
- If a colour-blind woman marries a person whose mother is colour-blind, then what is the probability of colour blindness in their offspring?
- CBSE Compartment XII - 2025
- Principles of Inheritance and Variation
- Find the magnetic field at a point 5 cm away from a long straight wire carrying current \( I = 20\,A \).
Show that the following lines intersect. Also, find their point of intersection:
Line 1: \[ \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} \]
Line 2: \[ \frac{x - 4}{5} = \frac{y - 1}{2} = z \]
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Three Dimensional Geometry
View More Questions