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There are 27 chocolates in a box, all identically shaped. There 4 are filled with nuts, 8 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting a solid chocolate candy followed by a nut candy.

Respuesta :

Answer:

Therefore the required probability is [tex]\frac{30}{351}[/tex].

Step-by-step explanation:

Two events are dependents event if the occurrence of one of them has effect on the probability of the other.

If A and B are dependents,

then,

P(AB)=P(A)P(B).

Given that,

There are 27 chocolates in a box.

Number of nuts chocolates = 4

Number of caramel chocolates = 8

Number of solid chocolates= 15.

The probability of that a solid candy is drawn is

[tex]=\frac{\textrm{Number of solid chocolate}}{\textrm{Total number of chocolate}}[/tex]

[tex]=\frac{15}{27}[/tex].

After selecting a solid chocolate, the number of chocolate is= (27-1)=26.

The probability that a nut candy is drawn is

[tex]=\frac{\textrm{Number of nut chocolate}}{\textrm{Total number of chocolate}}[/tex]

[tex]=\frac{4}{26}[/tex]

[tex]=\frac{2}{13}[/tex]

Therefore the required probability is

[tex]=\frac{15}{27}\times\frac{2}{13}[/tex]

[tex]=\frac{30}{351}[/tex]

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