The table with details of the ticket status for the various events is attached as an image
Part A
We have to determine for which sport probability of being sold out is 0.4
Probability = [tex]\frac{Number of Favorable Outcomes}{Number of Possible Outcomes}[/tex]
Let's determine the probability of being sold out for each of the sports
Probability (Rugby Sevens being sold out) = [tex]\frac{Number of events in which Rugby Sevens is sold out}{Total Events}[/tex]
⇒ Probability (Rugby Sevens being sold out) = [tex]\frac{3}{5}[/tex]
⇒ Probability (Rugby Sevens being sold out) = 0.6
Probability (Junior Athletics being sold out) = [tex]\frac{Number of events in which Junior Athletics is sold out}{Total Number of Events}[/tex]
⇒ Probability (Junior Athletics being sold out) = [tex]\frac{3}{5}[/tex]
⇒ Probability (Junior Athletics being sold out) = 0.6
Probability (Volleyball being sold out) = [tex]\frac{Number of events in which Volleyball is sold out}{Total Number of Volleyball Events}[/tex]
⇒ Probability (Volleyball being sold out) = [tex]\frac{2}{5}[/tex]
⇒ Probability (Volleyball being sold out) = 0.4
Hence, for Volleyball the probability of being sold out is 0.4
Part B
Probability of both Rugby 7s and Junior Athletics being sold out = Probability of Rugby 7s being sold out × Probability of Junior Athletics being sold out
Substituting the individual probabilities from Part A in above equation
⇒ Probability of both Rugby 7s and Junior Athletics being sold out = [tex]\frac{3}{5}[/tex] × [tex]\frac{3}{5}[/tex]
⇒ Probability of both Rugby 7s and Junior Athletics being sold out = [tex]\frac{9}{25}[/tex]
Hence, the probability of both Rugby 7s and Junior Athletics being sold out is [tex]\frac{9}{25}[/tex]
