In a throw of three dice,the probability that | vedclass

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

Question

(B) The total number of outcomes when throwing three dice is $6^3 = 216$.Let $E$ be the event that at least one die shows up $1$.It is easier to calcu

Vedclass · Accepted Answer

$\frac{91}{216}$

Vedclass · Answer

(B) The total number of outcomes when throwing three dice is $6^3 = 216$.Let $E$ be the event that at least one die shows up $1$.It is easier to calculate the probability of the complement event $E'$,which is the event that no die shows up $1$.For a single die,the probability of not getting a $1$ is $\frac{5}{6}$.Since the three dice are independent,the probability that none of the three dice show $1$ is $\left( \frac{5}{6} \right)^3 = \frac{125}{216}$.Therefore,the probability of the event $E$ is $P(E) = 1 - P(E') = 1 - \frac{125}{216} = \frac{216 - 125}{216} = \frac{91}{216}$.

In a throw of three dice,the probability that at least one die shows up $1$,is

Similar Questions

One ticket is drawn at random out of $30$ tickets numbered from $1$ to $30.$ Find the probability that the number on the ticket is a multiple of $5$ or $7.$

The probability of getting heads in all the three trials,when a balanced coin is tossed thrice,is

In order to get at least one head with a probability $\ge 0.9$,the minimum number of times a coin needs to be tossed is:

$A$ dice is thrown twice. The probability of getting $4, 5$ or $6$ in the first throw and $1, 2, 3$ or $4$ in the second throw is

$A$ bag contains $4$ white,$5$ red,and $6$ black balls. If two balls are drawn at random,then the probability that one of them is white is

Vedclass Test Series

Exam Paper Generator

Online Exam Module