Home
Class 12
MATHS
A ship is fitted with three engines E1,E...

A ship is fitted with three engines `E_1,E_2 and E_3`. The engines function independently of each other with respective probabilities `1/2, 1/4, and 1/4`. For the ship to be operational at least two of its engines must function. Let `X` denote the event that the ship is operational and let `X_1, X_2 and X_3` denote, respectively, the events that the engines `E_1, E_2 and E_3` are function. Which of the following is/are true? (a) `P(X_1^c "|"X)=3/(16)` (b)`P`(exactly two engines of the ship are functioning `"|"X` ) `=7/8` (c) `P(X"|"X_2)=5/6` (d) `P(X"|"X_1)=7/(16)`

A

`P(X_(1)^(C)//X)=3/16`

B

P (exactly two engines of the ship are functioning X `=7/8`

C

`P(X|X_(1))=5/16`

D

`P(X|X_(1))=7/16`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`P(X_(1))=1/2,P(X_(2))=1/4,P(X_(3))=1/4`
`P(X)=P(X_(1)nnX_(2)nnX_(3))+P(X_(1)nnX_(2)^(C)nnX_(3))`
`+P(X_(1)^(C)nnX_(2)nnX_(3))+P(X_(1)nnX_(2)nnX_(3)^(C))=1/4`
(1) `P(X_(1)^(C)//X)=(P(XnnX_(1)^(C)))/(P(X))=(1//32)/(1//4)=1/8`
(2) P [exactly two engines of the shp are functioning
`|X]=(7//32)/(1//4)=7/8`
(3) `P((X)/(X_(2)))=(P(XnnX_(2)))/(P(X_(2)))=(5//32)/(1//4)=5/8`
(4) `P((X)/(X_(1)))=(P(XnnX_(1)))/(P(X_(1)))=(7//32)/(1//2)=7/16`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|28 Videos

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise JEE Advanced|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

Similar Questions

Explore conceptually related problems

Find the range of the following functions: f(x)=(e^(x))/(1+absx),xge0 [.] denotes the greatest integer function.

E and F are two independent events. The probability that both e and F happen is 1/12 and the probability that neither E nor F happens is 1/2. Then

Statement -1 : Let E_1, E_2, E_3 be three events such that P(E_1)+P(E_2)+P(E_3)=1, " then " E_1, E_2, E_3 are exhaustive events. Statement-2 if the events E_1, E_2 " and " E_3 be exhaustive events, then P(E_1cupE_2cupE_3)=1

Differentiate the following function tan^(-1)(e^x) with respect to x

Suppose E_1, E_2 and E_3 be three mutually exclusive events such that P(E_i)=p_i" for " i=1, 2, 3 . P(none of E_1, E_2, E_3 ) equals

Let E=(1,2,3,4) and F-(1,2) . Then the number of onto functions from E to F is:

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.

The letters of the word PRABABILITY are written down at random in a row. Let E_1 denotes the event that two Is are together and E_2 denotes the event that B ' s are together, then P(E_1)=P(E_2=3/(11) (b) P(E_1nnE_2)=2/(55) P(E_1uuE_2)=(18)/(55) (d) P((E_1)/(E_2))=1/5

Suppose E_1, E_2 and E_3 be three mutually exclusive events such that P(E_i)=p_i" for "i=1, 2, 3 . If p_1, p_2 and p_3 are the roots of 27x^3-27x^2+ax-1=0 the value of a is

Suppose that E_1 and E_2 are two events of a random experiment such that P(E_(1))=1/4 , P(E_2 |E_1) =1/2 and P(E_1 |E_2)=1/4 . Observe the lists given below : The correct matching of the list I from the list II is :