probability question

[mitchk127]

There is a daily flight from paradise Island to Melbourne. The Probability of thre flight departing on time, given that there is fine weather on the isaland, is 0.8 and the probability of the flight departing on time, given that the weather on the island is not fine is 0.6. In March the probability of a day being fine is 0.4. Find the probability that on a particular day in March

(a) the flight from Paradise Island departs on time.

(b) the weather is fine on Paradise Island, given that the flight departs on time.

Any help would be appreciated

 

[Dr.Peterson]

Do you see that P(on time) = P((fine weather and on time) or (bad weather and on time))? Can you break that up and calculate the parts?

If not, please tell us what ideas you have tried, and what happened; or in some other way tell us why you are stuck, and what you know that might be of use.

 

[Sumeet]

(a) case 1) weather is fine and flight departs on time = 0.4 x 0.8 = 0.32
case 2) weather is not fine and flight departs on time = 0.6 x 0.6 = 0.36
total probablity that flight departs on time = 0.32 + 0.36 = 0.68

(b) 0.4 / 0.68 = 0.588

 

[Dr.Peterson]

Check your answer to part (b). If necessary, write out the definition of the conditional probability and make sure you are following that.

 

[pka]

There is a daily flight from paradise Island to Melbourne. The Probability of thre flight departing on time, given that there is fine weather on the isaland, is 0.8 and the probability of the flight departing on time, given that the weather on the island is not fine is 0.6. In March the probability of a day being fine is 0.4. Find the probability that on a particular day in March
(b) the weather is fine on Paradise Island, given that the flight departs on time.

(a) case 1) weather is fine and flight departs on time = 0.4 x 0.8 = 0.32
case 2) weather is not fine and flight departs on time = 0.6 x 0.6 = 0.36
total probablity that flight departs on time = 0.32 + 0.36 = 0.68
(b) 0.4 / 0.68 = 0.588

Sumeet, Have you missread part b)?
$\displaystyle \mathscr{P}(\text{weather is fine}|\text{flight departs on time})$
Your work in part a) is correct. $\displaystyle \mathscr{P}(\text{flight departs on time})=0.68$
So what is $\displaystyle \mathscr{P}(\text{weather is fine}|\text{flight departs on time})~?$