After observing the defects within individual candies in many bags of M&Ms, it h

Question

After observing the defects within individual candies in many bags of M&Ms, it has been determined that 11% of all candies are defective, that the probability of observing an M&M with a missing letter is 22%, and the probability of observing a cracked M&M given that you already know it is defective is 70%. What is the probability that you randomly select an M&M that is cracked? and a helpful hint for the probability question that involves m&m's -- a cracked m&m is considered to be defective as well, though the reverse need not be true. Equivalently, a cracked m&m is a type of defective m&m. 0.077 0.700 0 0.770 After observing the defects within individual candies in many bags of M&Ms, it has been determined that 11% of all candies are defective, that the probability of observing an M&M with a missing letter is 22%, and the probability of observing a cracked M&M given that you already know it is defective is 70%. What is the probability that you randomly select an M&M that is cracked? and a helpful hint for the probability question that involves m&m's -- a cracked m&m is considered to be defective as well, though the reverse need not be true. Equivalently, a cracked m&m is a type of defective m&m. 0.077 0.700 0 0.770

Explanation / Answer

sol)

probability that 11% of all candies are defective

ie P(D) =11%

probability of observing a cracked M&M given that you already know it is defective is 70%

P(C/D)= 70%

probability that you randomly select an M&M that is cracked

P(C/D) =P(C and D) / P(D)

P(C/D) = (P(C)P(D) )/ P(D)

P(C/D) =P(C)

Hence P(C) =0.7

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