Question

In a forest 20% of mushrooms are red, 50% brown and 30% white. A red mushroom is poisonous with a probability of 20%. A mushroom that is not red is poisonous with a probability of 5%. What is the probability that a poisonous mushroom in the forest is red

Answer 1

Answer:

20/100

Step-by-step explanation:

that is, in the question they have given that the probability of non red=20% so the total no.of mushroom in the forest is 100%(including poisonous mushroom)

Answer 2

Answer: 0.5

Step-by-step explanation:

Let R= mushrooms are red

R' =mushrooms are not red

P= poisonous

B= Brown mushroom

W =white mushroom

Given : P(R)=0.20 and P(B)=0.50  , P(W)=0.30

P(R')=P(B) + P(W)=0.50 + 0.30 = 0.80

P(P|R)=0.20

P(P|R')=0.05

Using Bayes theorem , our required probability is

$P(R|P)=\dfrac{P(P|R)\times P(R)}{P(P|R)\times P(R)+P(P|R')\times P(R')}\\\\=\dfrac{0.20\cdot 0.20}{0.20\cdot 0.20+0.05\cdot 0.80}=0.5$

Hence, the probability that a poisonous mushroom in the forest is red =0.5