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Problem of the Week
Problem A
Fishing for Prizes

Atharv is playing a game at the school fun fair. There are \(20\) bowls with a different fish in each bowl. Atharv throws a ping pong ball, and if it lands in a fishbowl, then he wins the fish in that bowl. The fishbowls and the fish contained in each bowl are shown below.

betta fish guppy guppy guppy goldfish
guppy clown fish goldfish betta fish guppy
tetra betta fish tetra clown fish minnow
guppy goldfish tetra guppy betta fish

Assume that every throw lands a ball into a fishbowl and each bowl has an equal chance of being the one that the ball lands in.

  1. Which fish is most likely to be won by Atharv?

  2. Which fish is least likely to be won by Atharv?

  3. Which fish are equally likely to be won by Atharv?

  4. Is it likely that Atharv will win a clown fish?

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