Conditional Probabilities

What is the probability of randomly selecting a student who received a sweater as a gift?

• $P\left(Sweater\right)=\frac{23}{76}$

• $P\left(Sweater\right)=\frac{46}{76}$

• $P\left(Sweater\right)=\frac{5}{23}$

• $P\left(Sweater\right)=\frac{5}{46}$

What is the probability of randomly selecting a student who received a socks as a gift and was surprised?

• $P\left(Socks\ \cup Surprised\right)=\frac{56}{76}$

• $P\left(Socks\ \cap Surprised\right)=\frac{42}{76}$

• $P\left(Socks\ \cap Surprised\right)=\frac{32}{76}$

• $P\left(Socks\ \cup Surprised\right)=\frac{88}{76}$

What is the probability that a randomly selected student received underwear as a gift or was not surprised?

• $P\left(Underwear\cap Surprised^C\right)=\frac{2}{76}$

• $P\left(Underwear\cup Surprised^C\right)=\frac{2}{11}$

• $P\left(Underwear\cup Surprised^C\right)=\frac{39}{76}$

• $P\left(Underwear\cup Surprised^C\right)=\frac{9}{46}$

Given a student was surprised with the gift, what is the probability that he or she got socks?

• $P\left(Surprised\left|Socks\right|\right)=\frac{32}{42}$

• $P\left(Socks\left|Surprised\right|\right)=\frac{32}{46}$

• $P\left(Surprised\left|Socks\right|\right)=\frac{32}{76}$

• $P\left(Surprised\left|Socks\right|\right)=\frac{8}{19}$

What is the probability that saw Frozen 2?

• $P\left(Frozen\ 2\right)=\frac{32}{116}$

• $P\left(Frozen\ 2\right)=\frac{32}{238}$

• $P\left(Frozen\ 2\right)=\frac{32}{57}$

• $P\left(Frozen\ 2\right)=\frac{57}{238}$

What is the probability of randomly selecting a student who saw Star Wars and an Evening Show?

• $P\left(Star\ Wars\cap Evening\ Show\right)=\frac{85}{238}$

• $P\left(Star\ Wars\cap Evening\ Show\right)=\frac{122}{238}$

• $P\left(Star\ Wars\cup Evening\ Show\right)=\frac{211}{238}$

• $P\left(Star\ Wars\cup Evening\ Show\right)=\frac{85}{145}$

What is the probability of randomly selecting a student who saw Jumanji or a Matinee?

• $P\left(Jumanji\cup Matinee\right)=\frac{24}{238}$

• $P\left(Jumanji\cap Matinee\right)=\frac{12}{238}$

• $P\left(Jumanji\cap Matinee\right)=\frac{24}{116}$

• $P\left(Jumanji\cup Matinee\right)=\frac{128}{238}$

Given that a student saw a Matinee, what is the probability of randomly selecting a student who saw Star Wars?

• $P\left(Matinee\ \left|Star\ Wars\right|\right)=\frac{60}{145}$

• $P\left(Star\ Wars\ \left|Matinee\right|\right)=\frac{60}{116}$

• $P\left(Star\ Wars\ \left|Matinee\right|\right)=\frac{60}{145}$

• $P\left(Star\ Wars\ \left|Matinee\right|\right)=\frac{60}{238}$

Given a student saw Frozen 2, what is the probability of randomly selecting a student that went to a evening show?

• $P\left(Evening\ Show\left|Frozen\ 2\right|\right)=\frac{25}{238}$

• $P\left(Evening\ Show\left|Frozen\ 2\right|\right)=\frac{25}{57}$

• $P\left(Evening\ Show\left|Frozen\ 2\right|\right)=\frac{25}{122}$

• $P\left(Frozen\ 2\left|Evening\ Show\right|\right)=\frac{32}{238}$

What is the probability of randomly selecting a student who went Ice Skating?

• $P\left(Ice\ Skating\right)=\frac{42}{96}$

• $P\left(Ice\ Skating\right)=\frac{42}{55}$

• $P\left(Ice\ Skating\right)=\frac{42}{137}$

• $P\left(Ice\ Skating\right)=\frac{55}{137}$