Five numbers, \(x_1, x_2, x_3, x_4, x_5\) are randomly selected from the numbers \(1, 2, 3\),….., \(18\) and are arranged in the increasing order \((x_1<x_2<x_3<x_4<x_5)\). The probability that \(x_2 = 7\) and \(x_4 = 11\) is:
- \(\frac{1}{136}\)
- \(\frac{1}{72}\)
- \(\frac{1}{68}\)
- \(\frac{1}{34}\)
The Correct Option is C
Solution and Explanation
The number of Total cases
=\(^{18}C_5\)
Favourable cases
\(^6C_1\) \(^3C_1\) \(^7C_1\)
\((Select \;x_1)\) \((Select \;x_3)\) \((Select \;x_5)\)
\(P =\frac{ 6.3.7}{^{18}C_5}\)
= \(\frac{1}{68}\)
Hence, the correct option is (C): \(\frac{1}{68}\)
Top Questions on Probability
- A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?
- MHT CET - 2025
- Mathematics
- Probability
- A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?
- BITSAT - 2025
- Mathematics
- Probability
- A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?
- BITSAT - 2025
- Mathematics
- Probability
- A box contains 5 red balls and 4 green balls. Two balls are drawn one after another without replacement. What is the probability that the second ball is green, given that the first ball drawn was red?
- BITSAT - 2025
- Mathematics
- Probability
- Two numbers are selected at random (without replacement) from the first 6 natural numbers. What is the probability that the difference of the numbers is less than 3?
- BITSAT - 2025
- Mathematics
- Probability
Questions Asked in JEE Main exam
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
For $ \alpha, \beta, \gamma \in \mathbb{R} $, if $$ \lim_{x \to 0} \frac{x^2 \sin \alpha x + (\gamma - 1)e^{x^2} - 3}{\sin 2x - \beta x} = 3, $$ then $ \beta + \gamma - \alpha $ is equal to:
The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank is _________ cm. (Take \( g = 10 \, {m/s}^2 \)).
- JEE Main - 2025
- System of Particles & Rotational Motion
- 'X' is the number of acidic oxides among $ VO_2, V_2O_3, CrO_3, V_2O_5 $ and $ Mn_2O_7 $. The primary valency of cobalt in $ [Co(H_2NCH_2CH_2NH_2)_3]_2 (SO_4)_3 $ is Y. The value of X + Y is :
- JEE Main - 2025
- Inorganic chemistry
- The kinetic energy of translation of the molecules in 50 g of CO\(_2\) gas at 17°C is:
- JEE Main - 2025
- The Kinetic Theory of Gases
Concepts Used:
Probability
Probability is defined as the extent to which an event is likely to happen. It is measured by the ratio of the favorable outcome to the total number of possible outcomes.
The definitions of some important terms related to probability are given below:
Sample space
The set of possible results or outcomes in a trial is referred to as the sample space. For instance, when we flip a coin, the possible outcomes are heads or tails. On the other hand, when we roll a single die, the possible outcomes are 1, 2, 3, 4, 5, 6.
Sample point
In a sample space, a sample point is one of the possible results. For instance, when using a deck of cards, as an outcome, a sample point would be the ace of spades or the queen of hearts.
Experiment
When the results of a series of actions are always uncertain, this is referred to as a trial or an experiment. For Instance, choosing a card from a deck, tossing a coin, or rolling a die, the results are uncertain.
Event
An event is a single outcome that happens as a result of a trial or experiment. For instance, getting a three on a die or an eight of clubs when selecting a card from a deck are happenings of certain events.
Outcome
A possible outcome of a trial or experiment is referred to as a result of an outcome. For instance, tossing a coin could result in heads or tails. Here the possible outcomes are heads or tails. While the possible outcomes of dice thrown are 1, 2, 3, 4, 5, or 6.