Question

A professional baseball team will play 1 game Saturdayand 1 game Sunday. A sportswriter estimates the teamhas a 60$\%$ chance of winning on Saturday but only a 35$\%$ chance of winning on sunday. Using the sportswriter's estimates, what is the probability that the team will lose both games?

• A. $12$
• B. $21$
• C. $25$
• D. $26$
• E. $39$

Answer 1

The correct option is D $26$

$P\left(winonsaturday\right)=60\%\therefore P\left(loseonsaturday\right)=40\%=\left(\frac{4}{10}\right)=\left(\frac{2}{5}\right)P\left(winonsunday\right)=35\%\therefore P\left(loseonsunday\right)=65\%=\left(\frac{65}{100}\right)=\left(\frac{13}{20}\right)P\left(losebothgames\right)P\left(loseonsaturday\right)\cdot P\left(loseonsunday\right)=\left(\frac{2}{5}\right)\cdot \left(\frac{13}{20}\right)=\left(\frac{26}{100}\right)=26\%$