Question

1.4 Level 2 Skill Checks: Probability

The table below shows which sports events have sold out and which have not. 




Event

1

Event

2

Event

3

Event

4

Event

5

Rugby 7s

Sold Out

Not Sold Out

Not Sold Out

Sold Out

Sold Out

Junior

Athletics

Sold Out

Sold Out

Not Sold Out

Not Sold Out

Sold Out

Volley Ball

Sold Out

Not Sold Out

Not Sold Out

Not Sold Out

Sold Out


Which sport has a 0.4 chance of being sold out?

 

Select...


What is the probability of both Rugby 7s and Junior Athletics being sold out? 

Give your answer as a fraction.

© bksb 2018

Answer 1

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 =
`(Number of Favorable Outcomes)/(Number of Possible Outcomes)`

Let's determine the probability of being sold out for each of the sports

Probability (Rugby Sevens being sold out) =
`(Number of events in which Rugby Sevens is sold out)/(Total Events)`

⇒ Probability (Rugby Sevens being sold out) =
`(3)/(5)`

⇒ Probability (Rugby Sevens being sold out) = 0.6

Probability (Junior Athletics being sold out) =
`(Number of events in which Junior Athletics is sold out)/(Total Number of Events)`

⇒ Probability (Junior Athletics being sold out) =
`(3)/(5)`

⇒ Probability (Junior Athletics being sold out) = 0.6

Probability (Volleyball being sold out) =
`(Number of events in which Volleyball is sold out)/(Total Number of Volleyball Events)`

⇒ Probability (Volleyball being sold out) =
`(2)/(5)`

⇒ 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 =
`(3)/(5)` ×
`(3)/(5)`

⇒ Probability of both Rugby 7s and Junior Athletics being sold out =
`(9)/(25)`

Hence, the probability of both Rugby 7s and Junior Athletics being sold out is
`(9)/(25)`