If a fair coin is tossed two times, the probability that the first or the second toss will be heads is ________ (rounded off to two decimal places).
Correct Answer: 0.75
Solution and Explanation
The probability of getting heads on either toss is:
\( P(\text{first head}) = \frac{1}{2}, \quad P(\text{second head}) = \frac{1}{2}. \)
Using the formula for the probability of either event occurring:
\( P(\text{first or second head}) = P(\text{first head}) + P(\text{second head}) - P(\text{both heads}), \)
\( P(\text{both heads}) = \frac{1}{4}. \)
Thus:
\( P = \frac{1}{2} + \frac{1}{2} - \frac{1}{4} = 0.75. \)
Top Questions on Probability
Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let \( A_1 \): People with good health,
\( A_2 \): People with average health,
and \( A_3 \): People with poor health.
During a pandemic, the data expressed that the chances of people contracting the disease from category \( A_1, A_2 \) and \( A_3 \) are 25%, 35% and 50%, respectively.
Based upon the above information, answer the following questions:
(i) A person was tested randomly. What is the probability that he/she has contracted the disease?}
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category \( A_2 \)?- If A and B are two events such that $P(B) = \frac{1}{5}$, $P(A | B) = \frac{2}{3}$ and $P(A \cup B) = \frac{3}{5}$, then $P(A)$ is :
- If \( P(A) = \frac{1}{5}, P(B) = \frac{3}{5} \) and \( P(A \cap B) = \frac{2}{5} \), then \( P(A' \cup B') \) is :
- Bag I contains 4 white and 5 black balls. Bag II contains 6 white and 7 black balls. A ball drawn randomly from Bag I is transferred to Bag II and then a ball is drawn randomly from Bag II. Find the probability that the ball drawn is white.
- A meeting will be held only if all three members A, B and C are present. The probability that member A does not turn up is 0.10, member B does not turn up is 0.20 and member C does not turn up is 0.05. The probability of the meeting being cancelled is:
Questions Asked in IIT JAM BT exam
- Ammonia is synthesized in the Haber process in the following reaction.
$π_2 (π) + 3π»_2 (π) β 2ππ»_3(π)$
The temperature above which the reaction becomes spontaneous is __________ πΎ (rounded off to one decimal place).
($\bigtriangleup π»^0 = β92.2 ππ½, \bigtriangleup π^0 = β199 π½πΎ^{ β1}$ ) - A cylinder contains 50 πΏ of an ideal gas at a pressure of 50 ππ‘π. Assuming that the temperature remains unchanged, the volume of the gas at 1 ππ‘π is __________ πΏ (rounded off to the nearest integer).
- IIT JAM BT - 2024
- Gas Laws
- Ionic character of the covalent bonds in the compounds Cl2, HCl, NaCl, NaF follows the order
- IIT JAM BT - 2024
- Chemical bonding and molecular structure
- A box of mass 20 ππ is pulled at constant speed across a floor by a rope. The rope makes an angle of 45Β° with the horizontal. Assuming that friction is negligible, the work done in pulling the box by a distance of 20 π is _____ π½ (rounded off to the nearest integer). (Use $π = 9.8 ππ ^{β2}$)
- IIT JAM BT - 2024
- Friction
- The value of $\lim_{π₯β3}\frac{(π₯^2 β9)}{(π₯^2β4π₯+3 )} $ is (rounded off to the nearest integer).
- IIT JAM BT - 2024
- Limits and derivations