Question

Mary is writing letters to her friends Barry, who lives in Australia, and Nelly and Penny, who live overseas. She seals the letters in the envelopes but is called to the door and cannot remember which letter is in which envelope when she gets back. Since she is in a hurry and doesn’t have any spare envelopes, she just writes the three addresses on the three envelopes in a random order. She only has one international $3 stamp and two domestic $1 stamps, so she tosses a fair coin to decide whether the envelope addressed to Nelly or the envelope addressed to Penny receives the international stamp, and places a domestic stamp on the other two letters, posts them in the local posting box, and hopes for the best. The post office throws the envelope with insufficient postage in the bin and delivers the other two envelopes as addressed. ( Take note the stamp conditions )

What is the probability that Penny receives the correct letter?

What is the probability that at least one of Barry, Nelly and Penny receives the correct letter?

Answer 1

I think it's assumed from the information that Mary lives in Australia.

As there are 3 letters probability that letter written for penny is correct is 1/3. After toss there is 1/2 probability that letter written to penny Wil bear the stamp so the probability of her receiving correct letter is 1/3*1/2= 1/6

For the second question atleast one is said so let's find probability when no one receives correct letter

As the letters are haphazardly arranged probability of no one getting correct letter is 1/3.

If Barry is addressed with the correct letter he will receive it so this condition is not to be taken! There is a chance that Barry and Nelly receives incorrect letter but penny receives correct! Probability of this is 1/6(1/3*1/2) in this case letter for penny should be without stamp so as to get the result of none getting correct letter so this is 1/6*1/2= 1/12. Same is the case if Barry and penny receive wrong letter but Nelly receives right letter but is not delivered. 1/12

So total chances in which none get right letter is 1/3+1/12+1/12.

So it comes out to be 1/2. In rest cases that is 1-1/2 = 1/2 cases atleast one Wil get right letter