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At a carnival game, you randomly throw two darts at the board and break two balloons. What is the probability that both the balloons you break are purple? There are 15 balloons total. 4 are purple.

Respuesta :

4/15 of the balloons are purple. You have two darts. There are 105 combinations of hitting two balloons out of the 15. There are 6 combinations of purple balloons to be hit. This (Purple combinations over total combinations) is your probability. 6/105 simplified to 2/35 or 2:35
So your chance of picking the purple balloons, both purple, out is 2 in 35 or 2/35
Brainliest?
CintiaSalazar

Taking into account the definition of probability,

But you have to know that probability is the greater or lesser possibility of a certain event occurring.

In other words, probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

[tex]P(A)=\frac{number of favorable cases}{number of posibble cases}[/tex]

Two events A and B are dependent if the occurrence of one of them affects the occurrence of the other. For dependent events, the probability is:

P(A and B)= P(A)× P(B|A)

The notation P(B|A) means "the probability of B, given that A has occurred"

In this case:

  • P(A)= [tex]\frac{4 purple balloons }{15 balloons total} = \frac{4}{15}[/tex]
  • If the first balloon is purple, it means we have 3 purple left out of the remaining 14. Then P(B|A)= [tex]\frac{3}{14}[/tex]

Replacing:

P(A and B)= [tex]\frac{4}{15}[/tex] ×[tex]\frac{3}{14}[/tex]

Solving:

P(A and B)=[tex]\frac{2}{35}[/tex]

Finally, the probability that both the balloons you break are purple is [tex]\frac{2}{35}[/tex]

Learn more:

  • https://brainly.com/question/10546643?referrer=searchResults
  • https://brainly.com/question/554279?referrer=searchResults
  • https://brainly.com/question/16736719?referrer=searchResults

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