Ebru is an entrepreneur. She plans to start 2 different very small businesses in the next year. Both businesses are independent of each other, and each business has a $50 \%$ chance of being successful and a $50 \%$ chance of failing.

Each business will make Ebru $\$ 200$ if it succeeds or lose her $\$ 200$ if it fails.
if $X$ is a random variable that represents Ebru's profit from starting these 2 businesses, drag the bars to graph the probability distribution for all possible values of $X$.

Question

Ebru is an entrepreneur. She plans to start 2 different very small businesses in the next year. Both businesses are independent of each other, and each business has a $50 \%$ chance of being successful and a $50 \%$ chance of failing.

Each business will make Ebru $\$ 200$ if it succeeds or lose her $\$ 200$ if it fails.
if $X$ is a random variable that represents Ebru's profit from starting these 2 businesses, drag the bars to graph the probability distribution for all possible values of $X$.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the possible outcomes for Ebru's profit from starting two independent businesses. ‖ ‖ step 2 ⋮ Calculate the probability for each outcome using the rules of probability for independent events. ‖ ‖ step 3 ⋮ Construct the probability distribution for the random variable $X$ representing Ebru's profit. ‖ ∻1 Answer∻ ⚹ The probability distribution graph for $X$ will have bars at $-400$, $0$, and $400$ with respective probabilities calculated in step 2. ⚹ ∻Key Concept∻ ⚹Probability Distribution of Independent Events⚹ ∻Explanation∻ ⚹The probability distribution for the sum of independent random variables is found by considering all possible outcomes and their associated probabilities.◊What is the expected value of Ebru's profit from starting these 2 businesses?⍭ Generate me a similar question◊⚹

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