Mathematics · 2023
JEE Main · 13 April 2023, Shift 1 · Q18
A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If X denotes the…
A coin is biased so that the head is $\displaystyle 3$ times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $\displaystyle X$ denotes the number of tosses of the coin, then the mean of X is
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle \frac{21}{16}$
More from Probability
- Bag B_1 contains 6 white and 4 blue balls, Bag B_2 contains 4 white and 6 blue balls, and Bag B_3 contains 5 white and 5 blue balls. One of the bags…2025
- Let S={M=[a_i j], a_i j ∈{0,1,2}, 1 ≤ i, j ≤ 2} be a sample space and A={M ∈ S: M is invertible } be an event. Then P(A) is equal to2023
- Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up…2026
- Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ red, 4 black balls respectively. One of the urns is selected at random and a ball…2023
- A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire…2026
- Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space S={x ∈ Z: x(66-x) ≥ 5/9 M} and the…2023
- 25 % of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung…2023
- One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2,…2025
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.