(a) A child possesses a container filled with colored building blocks. She will select one block without looking. The odds against selecting a blue block are 4/7. What is the probability of selecting a blue block?
Answer:
The likelihood of selecting a blue block is 7/11.
Step-by-step explanation:
To find the probability of selecting a blue block,
Odds:
The odds of a given event is the ratio of the probability of that event occurring to the probability of its absence. This means it compares favorable outcomes to those that are unfavorably likely.
The odds of not selecting a blue block being 4/7 means that out of 11 scenarios, there will be 4 occasions when the block is not blue, and 7 when it is blue.
Thus, the probability of not selecting the blue block is 4/11.
Probability of selecting the blue block is the complement of 4/11 which equals 7/11.
(b) Amanda plays a role-playing game with her friends. She will roll dice to decide if her character accesses a treasure chest. The chance of her character unlocking this chest is 13/20. Determine the odds in favor of her character unlocking the treasure chest.
Answer:
The odds in favor of her character unlocking the treasure chest equal 13/7.
Step-by-step explanation:
The probability of Amanda's character unlocking the treasure chest is given as 13/20.
This indicates that in a total of 20 chances, there will be 13 instances where the character successfully opens the treasure chest, while the remaining 7 times, they will not succeed.
Favorable outcomes: 13
Unfavorable outcomes: 7
Consequently, the odds in favor of her character unlocking the treasure chest are 13/7.
