A box of chocolates contains 20 identically shaped chocolates. 5 of them are filled jelly, 3 are filled with caramel and 12 are filled with nuts. What is the probability that one chocolate chosen at random is filled with jelly, caramel or nuts?

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Answer 1 · 2017-12-14T08:35:54

$100 %$ $100%$

$P (J e l l y) or P (C a r a m e l) or P (N u t s)$ $P(Jelly) or P(Caramel) or P(Nuts)$

$= P (J e l l y) + P (C a r a m e l) + P (N u t s)$ $= P(Jelly) + P(Caramel) + P(Nuts)$ (Here, I used the or rule)

$= \frac{5}{20} + \frac{3}{20} + \frac{12}{20}$ $= 5/20 + 3/20 + 12/20$

$= 1$ $= 1$

Also, if you think about it, the only options are jelly, caramel and nuts.

But, the question is asking what is the probability for all of the only options.

Therefore, it is certain (i.e. $100 %$ $100%$ ) that either a jelly, caramel or nuts would be chosen.

Hope that makes sense!