Question

Seven chits are numbered 1 to 7. Four chits are drawn one by one with replacement. The probability that the least number appearing on any selected chit is 5, is
A. \[{(\dfrac{3}{7})^4}\]
B. \[{(\dfrac{6}{7})^3}\]
C. \[\dfrac{{(5x4x3)}}{{{7^3}}}\]
D. \[{(\dfrac{3}{7})^3}\]

Answer 1

Hint: Probability signifies the possibility. It is a branch of mathematics that addresses the emergence of a random event. The value is stated from zero to one. Probability was introduced in Maths to forecast how probable events are to occur.

Complete step by step solution: Probability can be described as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favourable outcomes can be expressed by x.
In probability, we use combination and permutation to resolve the problem in an easy way. We can term combination and permutation as two functions that are used to resolve probability problems with ease and also in less time.
Finding the probability that the least number appearing on any chosen chit is 5.
Given: Seven chits are numbered 1 to 7.
Four chits are drawn one at a time with replacement.
Total number of chits = 7
The event that the least number on any chosen chit is 5 [Given] is {5,6,7}.
So, the probability of 5 or 6, or 7 in one draw = \[\dfrac{3}{7}\]
Therefore, in each of the 4 draws, the probability that the chit contains 5, 6, 7 is \[{(\dfrac{3}{7})^4}\].

Option ‘A’ is correct

Note: Probability is used for predicting outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards. The probability formula describes the probability of the happening of an event. It is the ratio of favourable results to the total favourable results.

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