In a certain region, 46% of the population is female.It is known that 5% of males and 2% of females are left-handed.A person is chosen at random and found to be left-handed.What is the probability that this person is a male?

Answer 1

#"The Reqd. Prob."=135/181~~74.59%#.

Let, #F, M, and, L# be the events that a randomly chosen person

from the region is a Female, Male, and, Left handed, resp.

From what is given, we have,

#P(F)=46/100, P(L/M)=5/100, and P(L/F)=2/100#.
We deduce #P(M)=P(F')=1-P(F)=1-46/100=54/100#.
Now, #P(L)=P(F)P(L/F)+P(M)P(L/M)#,
#=46/100*2/100+54/100*5/100#,
#=(92+270)/10000#.
# rArr P(L)=362/10000#.

By Definition,

#P(M/L)=(P(MnnL))/(P(L)), &, P(L/M)=(P(L nnM))/(P(M))#.
#:. P(M/L)-:P(L/M)=(P(M))/(P(L))#.
#rArr"The Reqd. Prob."=P(M/L)=P(L/M)*(P(M))/(P(L))#,
#={(5/100)(54/100)}/(362/10000)#,
#=135/181#.
#:. "The Reqd. Prob."=135/181~~74.59%#.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the probability that a left-handed person chosen at random is a male, we can use Bayes' theorem.

Let ( M ) be the event that the person is male, and ( L ) be the event that the person is left-handed.

Given:

  • Probability of being male (( P(M) )) = 54% = 0.54
  • Probability of being female (( P(F) )) = 46% = 0.46
  • Probability of being left-handed given male (( P(L|M) )) = 5% = 0.05
  • Probability of being left-handed given female (( P(L|F) )) = 2% = 0.02

We want to find ( P(M|L) ), the probability that the person is male given that they are left-handed.

Using Bayes' theorem:

[ P(M|L) = \frac{P(L|M) \times P(M)}{P(L)} ]

We can find ( P(L) ) using the law of total probability:

[ P(L) = P(L|M) \times P(M) + P(L|F) \times P(F) ]

Substitute the given values:

[ P(L) = 0.05 \times 0.54 + 0.02 \times 0.46 ]

[ P(L) = 0.027 + 0.0092 ]

[ P(L) = 0.0362 ]

Now, substitute the values into Bayes' theorem:

[ P(M|L) = \frac{0.05 \times 0.54}{0.0362} ]

[ P(M|L) = \frac{0.027}{0.0362} ]

[ P(M|L) \approx 0.7459 ]

Therefore, the probability that a left-handed person chosen at random is male is approximately ( 0.7459 ), or ( 74.59% ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7