Question

# three students decide to go sailing. Upon arriving at the boat however, they discover that it...

three students decide to go sailing. Upon arriving at the boat however, they discover that it is too dark below decks to clearly see the sails. Knowing that there are 3 jibs, 5 mains and 2 spinnakers on board, if each student goes below once and returns with a randomly picked sail, what is the probability that 2 or fewer jibs will end up above decks ?

without replacement

i started doing it like this: p(j≤3)=1 p(j≤2) + p(j=3)

p(j≤2)=1-p(j=3)

Probability that 2 or fewer jibs will end up above decks = Probability that at least one jib is picked by three students

= 1 - Probability that no jibs are picked by three students

= 1 - Probability that no jibs are picked by 1st student * Probability that no jibs are picked by 2nd student * Probability that no jibs are picked by 3rd student

= 1 - (7/10) * (6/ 9) * (5/ 8) (For 1st student, there are 3 jibs and 7 non-jibs. For 2nd student when mains or spinnaker is picked, there are 3 jibs and 6 non-jibs. For 3rd student when another mains or spinnaker is picked, there are 3 jibs and 5 non-jibs. )

= 1 - 7/24

= 17/24