A man is known to speak truth is 75% cases. If he throws an unbiased die a

Question

A man is known to speak truth is 75% cases. If he throws an unbiased die and tells his friend that it is a six, then the probability that it is actually a six, is

Options:

A . 16

B . 18

C . 34

D . 38

Answer: Option D
:
D
Let E denote the event that a six occurs and A be the event theat the man reports that it is a six. We have

P (E) = \frac{1}{6}, P (E^{'}) = \frac{5}{6}, P (\frac{A}{E}) = \frac{3}{4}

and

P (\frac{A}{E^{'}}) = \frac{1}{4}

.By Baye’s theorem

P (\frac{E}{A}) = \frac{P (E) . P (\frac{A}{E})}{P (E) . P (\frac{A}{E}) + P (E^{'}) . P (\frac{A}{E^{'}})} = \frac{(\frac{1}{6}) (\frac{3}{4})}{(\frac{1}{6}) (\frac{3}{4}) + (\frac{5}{6}) (\frac{1}{4})} = \frac{3}{8}

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. A father has three children with at least one boy. The probability that he has two boys and one girl is....

Question 2. One hundred identical coins, each with probability p of showing up heads are tossed once. If 0 < p < 1 ....head showing 51 coins, then the value of p is

Question 3. If (1+4p)4,(1−p)2,and (1−2p)2 are the probabilities of three mutually exclusive events , then the val....mutually exclusive events , then the value of p is

Question 4. Two events A and B have the probabilities 0.25 and 0.5 respectively. The probability that both A and B simultaneou....the probability that neither A and nor B occurs is

Question 5. Seven coupons are selected at random one at a time with replacement from 15 coupons numbered 1 to 15. The probability th....largest number appearing on a selected coupon is 9, is

Question 6. The probabilities of three mutually exclusive events A, B, C are given by 23,14, and 16 respectively. This sta....A, B, C are given by 23,14, and 16 respectively. This statement

Question 7. A random variable X has the following probability distribution XP(X=x)XP(X=x)0λ511λ13λ613λ25....X has the following probability distribution XP(X=x)XP(X=x)0λ511λ13λ613λ25λ715λ37λ817λ49λ then, λ is equal to

Question 8. A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to that gettin....9 heads, then the probability of getting 3 heads is

Question 9. A five digit number is formed with digits 0. 1. 2. 3. 4 without repetition. A number is selected at random, ....then the probability that it is divisible by 4 is

Question 10. Let `head` means 1 and `tail` means 2 and coefficients of the equation ax2+bx+c=0 are chosen by tossing a fair coin. The....the roots of the equation are non-real, is equal to

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers