A woman has 10 keys,out of which only one ope | vedclass

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

Question

(D) The total number of keys is $10$,and only $1$ key opens the lock.Since the keys are tried one after another without replacement,the probability th

Vedclass · Accepted Answer

$\frac{1}{10}$

Vedclass · Answer

(D) The total number of keys is $10$,and only $1$ key opens the lock.Since the keys are tried one after another without replacement,the probability that the $k$-th key works is the probability that the first $k-1$ keys fail and the $k$-th key succeeds.Let $F_i$ be the event that the $i$-th key fails and $S_i$ be the event that the $i$-th key succeeds.We want to find $P(F_1 \cap F_2 \cap F_3 \cap F_4 \cap F_5 \cap F_6 \cap S_7)$.Using the multiplication rule of probability:$P(F_1) = \frac{9}{10}$$P(F_2 | F_1) = \frac{8}{9}$$P(F_3 | F_1 \cap F_2) = \frac{7}{8}$$P(F_4 | F_1 \cap F_2 \cap F_3) = \frac{6}{7}$$P(F_5 | F_1 \cap F_2 \cap F_3 \cap F_4) = \frac{5}{6}$$P(F_6 | F_1 \cap F_2 \cap F_3 \cap F_4 \cap F_5) = \frac{4}{5}$$P(S_7 | F_1 \cap F_2 \cap F_3 \cap F_4 \cap F_5 \cap F_6) = \frac{1}{4}$Multiplying these probabilities:$P = \frac{9}{10} 	imes \frac{8}{9} 	imes \frac{7}{8} 	imes \frac{6}{7} 	imes \frac{5}{6} 	imes \frac{4}{5} 	imes \frac{1}{4} = \frac{1}{10}$.

$A$ woman has $10$ keys,out of which only one opens a lock. She tries the keys one after another (keeping aside the failed ones) until she succeeds in opening the lock. What is the probability that the seventh key works?

Similar Questions

If $A$ and $B$ are independent events and $P(A)=\frac{2}{3}$ and $P(B)=\frac{3}{5}$,then $P(A^{\prime} \cap B)$ is equal to:

If $A_1$ and $A_2$ are independent events and $P(A_1 \cup A_2) = 0.5$ and $P(A_1) = 0.2$,then $P(A_2) = $ . . . . . . .

Two urns identical in appearance contain respectively $3$ green and $2$ black balls and $2$ green and $5$ black balls. One urn is selected at random and a ball is drawn from it. The probability that it is black is

$A$ bag contains $19$ tickets numbered from $1$ to $19$. $A$ ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show an even number is:

$A$ bag contains $10$ similar balls,of which $4$ are blue and $6$ are red. Three balls are taken out at random from the bag one after the other without replacement. The probability that all the three balls drawn are red is

Vedclass Test Series

Exam Paper Generator

Online Exam Module