A concession stand at a movie theater offers soda and popcorn for sale. A survey shows that that 50% of moviegoers purchase a soda, 45% of moviegoers purchase popcorn, and 25% of the moviegoers purchase both soda and popcorn. We define the following events for a randomly chosen moviegoer: A:purchases a soda B: purchases popcorn For each of the events described below, provide an expression using events A and B; and compute their respective probabilities. (a) A randomly chosen moviegoer purchases a soda but not popcorn. (1 (b) A randomly chosen moviegoer purchases a soda or popcorn. (c) A randomly chosen moviegoer does not purchase anything.

A First Course in Probability (10th Edition)
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Please answer correctly and show all your work. Attached is the formula sheet you can use.
A concession stand at a movie theater offers soda and popcorn for sale. A survey shows that that
50% of moviegoers purchase a soda, 45% of moviegoers purchase popcorn, and 25% of the moviegoers
purchase both soda and popcorn.
We define the following events for a randomly chosen moviegoer:
A:purchases a soda
B: purchases popcorn
For each of the events described below, provide an expression using events A and B; and compute their
respective probabilities.
(a) A randomly chosen moviegoer purchases a soda but not popcorn. (1
(b) A randomly chosen moviegoer purchases a soda or popcorn.
(c) A randomly chosen moviegoer does not purchase anything.
Th
Transcribed Image Text:A concession stand at a movie theater offers soda and popcorn for sale. A survey shows that that 50% of moviegoers purchase a soda, 45% of moviegoers purchase popcorn, and 25% of the moviegoers purchase both soda and popcorn. We define the following events for a randomly chosen moviegoer: A:purchases a soda B: purchases popcorn For each of the events described below, provide an expression using events A and B; and compute their respective probabilities. (a) A randomly chosen moviegoer purchases a soda but not popcorn. (1 (b) A randomly chosen moviegoer purchases a soda or popcorn. (c) A randomly chosen moviegoer does not purchase anything. Th
Expert Solution
Step 1

Given that 

A=purchase soda

B=purchase popcorn 

P(A)=50% , P(B)=45% , P(A and B)=25%

 

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