# Video: Solving Word Problem Involving Theoretical Probability

Bassem plays a card game with his friend and the result can be either win, lose, or draw. Each time they play, the probability that Bassem will win is 0.5, and the probability he will lose is 0.3. If they play 50 games, what is the expected number that will end in a draw?

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### Video Transcript

Bassem plays a card game with his friends and the results can be either win, lose, or draw. Each time they play, the probability that Bassem will win is 0.5, and the probability that he will lose is 0.3. If they play 50 games, what is the expected number that will end in a draw?

The probability that Bassem will win is 0.5, about half the time. The probability that Bassem will lose is 0.3. And we have one other option: the probability that there will be a draw. We’re not given the probability of this event. We have to use what we already know to calculate that probability.

What we know is that the probability of all the options a, b, and c must add up to one. The options are that you win half the time, lose 0.3 of the time, and draw how often?

The probability that he will win plus the probability that he will lose is 0.8. One minus 0.8 equals 0.2. Bassem will draw 0.2 of the time. If he loses 0.2 of the time and they play 50 games, we can multiply 0.2 by 50 to find the expected number of games that will end in a draw. 0.2 times 50 equals 10.

We expect that 10 games would end in a draw.