For a customer to choose a chocolate cone it need to choose "Chocolate" (0.35 probability) and choose a cone (0.4 probability given he chose chocolate).
So, the get the probability of both, we multiply their probabilities:
![P=0.35\cdot0.4=0.14](https://tex.z-dn.net/?f=P%3D0.35%5Ccdot0.4%3D0.14)
Thus, the probability of a customer choosing a chocolate cone is, based on the image, 0.14 or 14%.
Well that would not work 5.25x2=10.5 5.25x3=15.75
(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.
The formula is given as;
![nP_r=\frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=nP_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.
Therefore, we would have;
![\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20nP_r%5CRightarrow_8P_5%20%5C%5C%20_8P_5%3D%5Cfrac%7B8%21%7D%7B%288-5%29%21%7D%5CRightarrow%5Cfrac%7B8%21%7D%7B3%21%7D%20%5C%5C%20_8P_5%3D%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes%5Cldots1%7D%7B3%5Ctimes2%5Ctimes1%7D%5CRightarrow%5Cfrac%7B40320%7D%7B6%7D%20%5C%5C%20_8P_5%3D6720%20%5Cend%7Bgathered%7D)
Therefore, if the order is relevant, this selection can be done in 6,720 ways.
(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;
![_nC_r=\frac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=_nC_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
The formula can now be applied as follows;
![\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20_nC_r%5CRightarrow_8C_5%20%5C%5C%20_8C_5%3D%5Cfrac%7B8%21%7D%7B%288-5%29%21%5Ctimes5%21%7D%20%5C%5C%20_8C_5%3D%5Cfrac%7B8%21%7D%7B3%21%5Ctimes5%21%7D%5CRightarrow%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes%5Cldots1%7D%7B%283%5Ctimes2%5Ctimes1%29%5Ctimes%285%5Ctimes4%5Ctimes%5Cldots1%29%7D%20%5C%5C%20_8C_5%3D%5Cfrac%7B40320%7D%7B6%5Ctimes120%7D%20%5C%5C%20_8C_5%3D56%20%5Cend%7Bgathered%7D)
If the order is not relevant, then the selection can be done in 56 ways.
Probability of a dice rolling a 4 = 1/6
Probability of a coin coming up tails = 1/2
now we multiply the two probabilities together to find what the probability of BOTH occurring at the same time is.
1/6 × 1/2 = 1/12
Answer is D. 1 over 12