A professional baseball team will play 1 game Saturday and 1 game Sunday. A sportswriter estimates the team has 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? (Note: Neither game can result in a tie.)
Question
A professional baseball team will play 1 game Saturday and 1 game Sunday. A sportswriter estimates the team has 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? (Note: Neither game can result in a tie.)
Solution
To find the probability that the team will lose both games, we need to multiply the probability of losing on Saturday by the probability of losing on Sunday.
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The probability of losing on Saturday is the complement of the probability of winning on Saturday. So, if the team has a 60% chance of winning on Saturday, it has a 40% (100% - 60%) chance of losing on Saturday.
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Similarly, the probability of losing on Sunday is the complement of the probability of winning on Sunday. So, if the team has a 35% chance of winning on Sunday, it has a 65% (100% - 35%) chance of losing on Sunday.
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Now, we multiply these two probabilities together to find the probability of both events happening. So, the probability of the team losing both games is 40% * 65% = 26%.
So, according to the sportswriter's estimates, the team has a 26% chance of losing both games.
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