terrence joined a book club to spend more quality time with his cousin. at the first meeting, club members…

terrence joined a book club to spend more quality time with his cousin. at the first meeting, club members recorded how many hours a week they typically read and whether they preferred e-readers or paperback books.\n\nthe probability that a club member reads at least 1 hour per week is 0.9, the probability that a club member prefers e-readers is 0.9, and the probability that a club member reads at least 1 hour per week or prefers e-readers is 1.\n\nwhat is the probability that a randomly chosen club member reads at least 1 hour per week and prefers e-readers?\n\nwrite your answer as a whole number, decimal, or simplified fraction.

terrence joined a book club to spend more quality time with his cousin. at the first meeting, club members recorded how many hours a week they typically read and whether they preferred e-readers or paperback books.\n\nthe probability that a club member reads at least 1 hour per week is 0.9, the probability that a club member prefers e-readers is 0.9, and the probability that a club member reads at least 1 hour per week or prefers e-readers is 1.\n\nwhat is the probability that a randomly chosen club member reads at least 1 hour per week and prefers e-readers?\n\nwrite your answer as a whole number, decimal, or simplified fraction.

Answer

Explanation:

Step1: Define events and formula

Let $A$ = reads at least 1 hour/week, $B$ = prefers e-readers. Use the addition rule: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Step2: Rearrange to solve for $P(A \cap B)$

Isolate the joint probability term: $$P(A \cap B) = P(A) + P(B) - P(A \cup B)$$

Step3: Substitute given values

Plug in $P(A)=0.9$, $P(B)=0.9$, $P(A \cup B)=1$: $$P(A \cap B) = 0.9 + 0.9 - 1$$

Step4: Calculate the result

Compute the arithmetic: $$P(A \cap B) = 0.8$$

Answer:

0.8