Question

A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue block are 4/7. What is the probability of choosing a blue block?
Amanda is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her character unlocking the treasure chest is 13/20. Find the odds in favor of her character unlocking the treasure chest.

Answer 1

(a) A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue block are 4/7. What is the probability of choosing a blue block?

Answer:

7/11 is the probability of choosing a blue block.

Step-by-step explanation:

We need the probability of choosing a blue block,

Odds:

The odds of an event is the ratio of the probability of an event to the probability of its complement. In other words, it is the ratio of favorable outcomes to unfavorable outcomes.

The odds against choosing a blue block are 4/7 means. In 11 chances, 4 events will happen in which blue block will not be chosen and 7 events will happen in which blue blocks will be chosen.

So, the probability of not choosing the blue block is 4/11.

Probability of choosing blue block: complement of 4/11 which is equal to 7/11.

(b) Amanda is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her character unlocking the treasure chest is 13/20. Find the odds in favor of her character unlocking the treasure chest.

Answer:

The odds in favor of her character unlocking the treasure chest are 13/7.

Step-by-step explanation:

The probability of Amanda's character unlocking the treasure chest is 13/20.

It means, in 20 total chances, 13 times an event will happen where Amanda's character unlocks the treasure chest while the rest 7 times, her character would not open treasure chest.

Favorable events: 13

Unfavorable events: 7

Hence, the odds in favor of her character unlocking the treasure chest are 13/7.