According to a survey compiled by TVFree America 59 of Ameri

According to a survey compiled by TV-Free America, 59% of Americans can name the three main characters from the classic comedy TV show called The Three Stooges but only 17% can name at least three justices of the U.S. Supreme Court. Suppose two Americans are selected at random.

Fill in the blanks.

The probability that both can name The Three Stooges is _(Answer 1)_ .

The probability that both can name at least three justices of the U.S. Supreme Court _(Answer 2)_ .

The probability that at least one of them can name at least three justices of the U.S. Supreme Court is _(Answer 3)_ .

Solution

P(person remember all 3 from three stooges)=0.59.

P(person remember atleast 3 justices of US)=0.17.

Answer 1: so probability that all 3 stooges are remembered by both person = 0.59*0.59 = 0.3481.

Answer 2: so probability that atleast 3 justices of US remembered by both person = 0.17*0.17 = 0.0289.

Answer 3: P(atleast 1 can remember 3 justices)= 1-P(no one can remember)= 1-0.83*0.83 = 1-0.6889 = 0.3111.