At the carnival, we found a bean bag toss booth. There's a 0.64 probability of throwing the bean bag into the outer ring, a 0.11 probability of throwing it into the middle ring, and the remaining probability throwing it into the center of the target. Tickets are awarded depending on which ring the bean bag lands in. We get 1 ticket for the outer ring, 2 tickets for the middle ring, and 3 tickets for the center. What is the expected value (number of tickets) we will get if we play the game 10 times

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13-07-2022
Mathematics

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At the carnival, we found a bean bag toss booth. There's a 0.64 probability of throwing the bean bag into the outer ring, a 0.11 probability of throwing it into the middle ring, and the remaining probability throwing it into the center of the target. Tickets are awarded depending on which ring the bean bag lands in. We get 1 ticket for the outer ring, 2 tickets for the middle ring, and 3 tickets for the center. What is the expected value (number of tickets) we will get if we play the game 10 times

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yogeshkumar49685 yogeshkumar49685 · Answer 1 · 2022-07-16T08:32:37+02:00

The expected value after 10 game at a carnival is 16.1 tickets.

Given the probabilities that bag lands into the outer ring, middle ring, center are 0.64, 0.11 and remaining. 1 ticket awarded for the outer, 2 for middle and 3 for middle.

We have to find the expected value we will get if we play the game 10 times.

Probability is the chance of happening an event among all the events possible. Value of probability lies between 0 and 1. The formula of probability is as under:

Probability=number of items/ total items in consideration.

Probability that bag lands in center is 1-0.64-0.11=0.25.

Expected value when game is played 1 time=1*0.64+2*0.11+3*0.25

=0.64+0.22+0.75

=1.61

Expected value when the game is played 10 times=10*1.61

=16.1 tickets.

Hence the expected value when game is played 10 times is 16.1 tickets.

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