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A drug company is about to start clinical trials of two new drugs that it has developed to help people to quit smoking.
Based on experience and current laboratory results, the drug company believes that there is a 70% chance that both drugs will be accepted and a 20% chance only one will be accepted.

If both are accepted the drug company will make \$10 million. If one is accepted the drug company will make a \$4 million profit, while if both are rejected they will lose \$2 million. What is the drug company's expected profit?

Is it:-

$7.2 million?

$7.6 million?

$10.0 million?

None of the above?

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    $\begingroup$ Please see the forum's policy on homework or similar questions. You are asked to show your reasoning in a draft answer and ask for comments. Just giving the question is not enough. $\endgroup$ – Nick Cox Sep 4 '13 at 11:17
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    $\begingroup$ Welcome to the site. For self study questions you should tell us what you have tried so far and where exactly you are stuck; see stats.stackexchange.com/tags/self-study/info $\endgroup$ – Peter Flom - Reinstate Monica Sep 4 '13 at 11:20
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Well, from a frequency table the expected value is given by

$E(X)=\sum_ia_ip(x_i)$

Where $a_i$ is the value of a particular outcome, $x_i$ is a particular outcome and $p(x_i)$ is its associated probability.

Can you solve it from there?

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  • $\begingroup$ I have given the answer since the tone of the question seems to indicate that the asker already has some idea of the answer. EDIT: I removed the explicit calculation as this is self study. $\endgroup$ – Simon Hayward Sep 4 '13 at 11:24

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