Scientists were trying out a new lie detection test based on a needle. The needle indicates red if it a lie and green if it’s true. For any person lying, there is a 75% chance of the needle pointing towards red. For a person not lying, there is a 90% chance of the needle pointing towards green. It is known that 10% of people who go for the test are lying. If a person who tests to have lied, If the probability that they actually lied is P, then 11P equals?
Answers
Given : The needle indicates red if it a lie and green if it’s true. For any person lying, there is a 75% chance of the needle pointing towards red. For a person not lying, there is a 90% chance of the needle pointing towards green. It is known that 10% of people who go for the test are lying.
If a person who tests to have lied, If the probability that they actually lied is P
To Find : Value of 11P
Solution:
Probability of red for liar = 0.75
Probability of green for liar = 0.25 ( 1 - 0.75 = 0.25)
Probability of green for not lying= 0.9
Probability of red for not lying = 0.1 ( 1 - 0.9 = 0.1)
Lying = 0.1 not lying = 0.9
a person who tests to have lied,
if lying (0.1)(0.75) = 0.075
if not lying (0.9)(0.1) = 0.09
probability that they actually lied is = (0.075) / (0.075 + 0.09)
= 75/165
= 5/11
P = 5/11
11P = 5
Learn More:
brainly.in/question/9066514
the probability that an event happens in one trial of an experiment is ...
brainly.in/question/8759895
Determine the experimental probability of getting a head (or a tail ...
brainly.in/question/18400413
Solution :-
- Red = Lie .
- Green = True .
Now, For any person lying, we have ,
- Red Probability = 75% = 75/100 = 0.75
- Green Probability = 25% = 25/100 = 0.25
and, For any person not lying, we have ,
- Red Probability = 10% = 10/100 = 0.1
- Green Probability = 90% = 90/100 = 0.9
now, given that ,
- People who go for the test are lying = 10% = 0.1
- P = probability of a person who tests to have actually lied .
then,
→Probability of a person who actually lied is = Number of favourable outcomes / Total Number of outcomes
→ P = (0.1 * 0.75) / (0.1*0.75 + 0.1*0.9)
→ P = 0.075/(0.075 + 0.09)
→ P = 0.075 / 0.165
→ P = 75 / 165
→ P = 5 / 11
hence,
→ Value of 11P = (5/11) * 11 = 5 (Ans.)
Learn more :-
7cm long stick cut in three pieces. Length of each piece is natural number.
What is the probability of forming triangl...
https://brainly.in/question/37342919
Ang, Ben, and Jasmin each have 5 blocks, colored red, blue, yellow, white, and green; and there are 5 empty boxes. Each ...
https://brainly.in/question/34973202
If a die is rolled twice, what is the probability that the sum of the points is more than 9
https://brainly.in/question/8806537