Question

A bowl contains 20 candies; 15 are chocolate and 5 are vanilla. You select 5 at random. What is the probability that all 5 are chocolate?

Answer 1

A bowl contains 20 candies; 15 are chocolate and 5 are vanilla.

If we select 5 candies, then the number of ways to select them is given by permutations.

The number of ways to select 5 candies is given by :-

^{15}P_5=\dfrac{15!}{(15-5)!}=\dfrac{15\times14\times13\times12\times11\times10!}{10!}=360360

15

P

5

=

(15−5)!

15!

=

10!

15×14×13×12×11×10!

=360360

The number of ways of selecting any 5 candies out of 20:-

\begin{lgathered}^{20}P_5=\dfrac{20!}{(20-5)!}\\\\=\dfrac{20\times19\times18\times17\times16\times15!}{15!}\\\\=1860480\end{lgathered}

20

P

5

=

(20−5)!

20!

=

15!

20×19×18×17×16×15!

=1860480

Now, the probability that all 5 are chocolate :-

=\dfrac{360360}{1860480}=0.193691950464\approx0.1937=

1860480

360360

=0.193691950464≈0.1937

Hence, the probability that all 5 are chocolate

Answer 2

Answer: 0.1937

Step-by-step explanation:

Given : A bowl contains 20 candies; 15 are chocolate and 5 are vanilla.

If we select 5 candies, then the number of ways to select them is given by permutations.

The number of ways to select 5 candies is given by :-

`^(15)P_5=(15!)/((15-5)!)=(15*14*13*12*11*10!)/(10!)=360360`

The number of ways of selecting any 5 candies out of 20:-

`^(20)P_5=(20!)/((20-5)!)\\\\=(20*19*18*17*16*15!)/(15!)\\\\=1860480`

Now, the probability that all 5 are chocolate :-

`=(360360)/(1860480)=0.193691950464\approx0.1937`

Hence, the probability that all 5 are chocolate =0.1937