Ram and Syam are friends. Probability that both will have same birthday is:
Show Hint
- \( \frac{364}{365} \)
- \( \frac{1}{365} \)
- \( \frac{1}{364} \)
- \( \frac{363}{365} \)
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Probability.
There are 365 days in a year (ignoring leap years), and each person has an equal chance of being born on any of these days. For the probability that Ram and Syam will have the same birthday, the first person (Ram) can have his birthday on any of the 365 days, but for Syam to have the same birthday, he must be born on the same day as Ram.
Step 2: Probability Calculation.
The probability that Syama's birthday matches Rama's birthday is: \[ P(\text{same birthday}) = \frac{1}{365} \] However, for both to have the same birthday, the event happens only after considering the first personas (Ram's) birthday choice, so the probability is \( \frac{364}{365} \) for Syam.
Step 3: Conclusion.
Thus, the probability that both Ram and Syam will have the same birthday is: \[ P(\text{same birthday}) = \frac{364}{365} \]
Top Questions on Probability
- The probability that a student buys a colouring book is 0.7, and a box of colours is 0.2. The probability that she buys a colouring book, given that she buys a box of colours, is 0.3. Find:
(i) The probability that she buys both the colouring book and the box of colours.
(ii) The probability that she buys a box of colours given she buys the colouring book. - A fruit box contains 6 apples and 4 oranges. A person picks out a fruit three times with replacement. Find:
(i) The probability distribution of the number of oranges he draws.
(ii) The expectation of the number of oranges. Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.
- 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:
Two persons are competing for a position on the Managing Committee of an organisation. The probabilities that the first and the second person will be appointed are 0.5 and 0.6, respectively. Also, if the first person gets appointed, then the probability of introducing a waste treatment plant is 0.7, and the corresponding probability is 0.4 if the second person gets appointed.
Based on the above information, answer the following
Questions Asked in AP POLYCET exam
- A prime number \( p \) divides \( a^2 \) where \( a \) is a positive integer, then
- AP POLYCET - 2025
- Prime and Composite Numbers
- Area of a sector of a circle with radius 4 cm and angle 30° is (use \( \pi = 3.14 \)):
- The solution of \( x - 2y = 0 \) and \( 3x + 4y - 20 = 0 \) is:
- AP POLYCET - 2025
- Linear Equations
- If assumed mean of a data is 47.5, \( \sum f_i d_i = 435 \) and \( \sum f_i = 30 \), then mean of that data is:
- AP POLYCET - 2025
- Arithmetic Mean
- The points \( (1,5), (2,3) \) and \( (-2, -11) \) form a: