Mrs. jones buys two toys for her son. the probability that the first toy is defective is `1/3`, and the probability that the second toy is defective given that the first toy is defective is `1/5`. what is the probability that both toys are defective?

Step-by-step explanation:

Let A denote the event of first  toy is defective and B denote the second toy is defective .

Given: The probability that the first toy is defective

The probability that the second toy is defective given that the first toy is defective  =

The formula to calculate the conditional probability is given by :

Hence, the required probability :

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560