Question

question 14
a couple plans to have four children. using a tree diagram, obtain the sample space. then, find the probability that the family has at least one boy.
a 13/16
b 1
c 13/4
d 15/16
question 15
a contractor is considering a sale that promises a profit of $29,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $1,000 with a probability of 0.3. what is the expected profit?
5 points

Explanation:

Step1: Recall the formula for expected value

The formula for expected value \(E(X)\) is \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) are the possible values and \(p_i\) are their corresponding probabilities.

Step2: Identify the values and probabilities

Here, \(x_1 = 29000\) with \(p_1=0.7\) and \(x_2=- 1000\) (since it's a loss) with \(p_2 = 0.3\).

Step3: Calculate the expected value

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Answer:

The expected profit is \(\$20000\)