If a coin is tossed seven times,then the prob | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The total number of outcomes when a coin is tossed $7$ times is $2^7 = 128$.We need to find the number of ways to get exactly $3$ heads such that

Vedclass · Accepted Answer

$\frac{5}{64}$

Vedclass · Answer

(A) The total number of outcomes when a coin is tossed $7$ times is $2^7 = 128$.We need to find the number of ways to get exactly $3$ heads such that no two heads are consecutive.Let the $4$ tails be represented as $T, T, T, T$. These create $5$ possible slots (including ends) where heads can be placed: $\_ T \_ T \_ T \_ T \_$.To ensure no two heads are consecutive,we must choose $3$ slots out of these $5$ available slots.The number of ways to choose $3$ slots out of $5$ is given by $\binom{5}{3} = \frac{5 	imes 4}{2 	imes 1} = 10$.Thus,the number of favorable outcomes is $10$.The probability is $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{10}{128} = \frac{5}{64}$.

If a coin is tossed seven times,then the probability of getting exactly three heads such that no two heads occur consecutively is

Similar Questions

Two numbers $a$ and $b$ are chosen at random from the set of the first $30$ natural numbers. The probability that $a^2 - b^2$ is divisible by $3$ is

$A$ bag contains $3$ red,$4$ white,and $5$ black balls. Three balls are drawn at random. The probability that they are of different colours is

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains all $4$ Kings.

$A$ basket contains $12$ apples in which $3$ are rotten. If $3$ apples are drawn at random simultaneously from it,then the probability of getting at most one rotten apple is

Three squares of a chessboard are chosen at random. The probability that two are of one colour and one is of another colour is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module