Probability help?

Question

1. The probability that a doctor correctly diagnosis a particular illness is 0.7. Given that the doctor makes an incorrect diagnosis the probability that the patient enters a law suit is 0.9.What is the probability that the doctor makes an incorrect diagnosis and the patient asues?

2. The probability that a married man watches a certain television show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show,given that his wife does is 0.7.Find the probability that
a. a married couple watches the show
b. a wife watches the show given that her husband does
c. at least one person of amarried couple will watch the show

thanks for the help.....i'm really getting a hard tym with this course.....

Answer 1

correctly diagnosis illness= 0.7
incorrectly diagnosis illness= 0.3

probability that the doctor makes an incorrect diagnosis and the patient asues = 0.9 * 0.3 = 0.27



a. a married couple watches the show = 0.5 * 0.7 = 0.35

b. a wife watches the show given that her husband does
= 0.4 * 0.5 = 0.2

c. at least one person of amarried couple will watch the show
= P( man & not wife) or P( not man & wife does) or P( both do)
= 0.4 * 0.5 + 0.6 * 0.5 + 0.4 * 0.5
= 0.7

I think

Answer 2

1.
P[wrong diagnosis] = 0.3
P[law suit | wrong diagnosis] = 0.9
find P[ wrong diagnosis & Law suit]

remember the definition for conditional probabilities:
P[a|b] = P[a & b]/P[b]

so...P[ wrong diagnosis & Law suit] = P[law suit | wrong diagnosis]*P[wrong diagnosis] = 0.27
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2.
Let M be the event that a married man watches the show
Let W be the event that a married woman watches the show

P[M] =0.4, P[W] = 0.5, P[ M | W ] = 0.7

a. find P[M & W] = P[M|W]*P[W] = 0.35
b. find P[ W | M ]
This uses Bayes' Rule which if you don't know you can figure out from the definition of conditional probability and the law of total probability. However, you've been given enough info to skip this. Just use conditional probabilities.

P[ W | M ] = P[ W & M] / P[M] = P[ M | W ]*P[W] / P[ M]
= 0.35/0.4 = 0.875

c. P[W or M ] = ?

remember this definition? P[A & B] = P[A] + P[B] - P[A or B]

P[W or M ] = P[M] + P[W] - P[M & W]
= 0.4 + 0.5 - 0.35
= 0.55

Answer 3

1. Probability of an incorrect diagnosis is 1 - 0.7 = 0.3. Probability of an lawsuit for a given diagnosis is 0.3*0.9 = .27. This doctor is gonna have trouble getting liability insurance.

2. a. (probability that wife watcheses)*(probability that husband does given that wife does) = 0.5*0.7 = .35
b. (probability that both watch)/(probability that husband does) = .35/0.4 = .85
c. (probability that husband does) + (probability that wife does) - (probability that both do) = 0.4 + 0.5 - 0.35 = 0.55

Answer 4

These relie on the idea of conditional probability.

1. P(C)=0.7 P(L | not C)=0.9

We want P(L and not C)=P(L | not C)x P(not C)

=0.9x0.3

2. I have looked at other submitted answers and they assume independence, which is not valid. There is not enough info to answer the question.

Answer 5

1) C = correct diagnosis, L = law suit

Given:
P(C) = 0.7
P(L/C') = P(L∩C')/P(C') = 0.9

P(C'∩L) = P(L/C') x P(C') = 0.9(1-0.7) = 0.27

2) M = a married man watches the tv show
W = a married woman watches the tv show

Given:
P(M) = 0.4
P(W) = 0.5
P(M/W) = P(M∩W)/P(W) = 0.7

a. P(M∩W) = P(M/W) x P(W) = 0.7(0.5) = 0.35

b. P(W/M) = P(W∩M)/P(M) = 0.35/0.4 = 0.875

c. P(MUW) = P(M) + P(W) - P(M∩W) = 0.4 + 0.5 - 0.35 = 0.55

Answer 6

1.
Correct-.7
Incorrect=x
Total of both= 1
Sues-.9
1.00-.70=.3
Sues-.9*.3=.27 or 27% of the time
2.
Married Man-.4
Married Women-.5
Both-.7
A=70 %
B=50 %
C=10%

Answer 7

1)(1- 0.7)*0.9=0.27

Answer 8

1. 0.3x0.9=0.27
2.
a)0.7x0.5=.35
b)0.4x0.5=0.2
c)1-[(1-0.4)(1-0.5)]=0.7