Mary and Josh have 100 dollars to invest. They are thinking between three investment alternatives. 1) to invest the 100 dollars for a sun screen factory; 2) to invest 100 dollars in the umbrella's factory or 3) to invest half in each company (sun screen and umbrella). The shares are priced at 10 dollars. If however in the next three months the weather is sunny the shares for the sun screen brand will hike to 20 dollars, and the umbrella's will be down to 5. In the other side, if the weather is rainy, the sun-screen shares will plunge to 5, and the umbrella will rise to 20. Suppose the probability for the next three months to be sunny is and to rain is . Josh is indifferent to risk, and Mary is averse, which investment alternative each one should choose? Please show the step behind the solution, thanks!

= 0,5 (1 ) = 0, 5