Final answer:
The probability of winning the lunch for your friends is 1/150. The probability of you attending the pizza lunch this month is 0.00445. The chances of you and your friends winning 3 pizza lunches in a row is 0.00000148.
Step-by-step explanation:
To calculate the probability of winning the lunch for your friends, we first need to find the probability of your ticket being selected. Since there are 150 students attending the rally, and you are one of them, the probability of your ticket being chosen is 1/150. Since you and your 5 friends have decided to share the pizza lunch no matter whose ticket is selected, the probability of you personally winning the lunch for your friends is 1/150.
To calculate the probability of you attending the pizza lunch this month, we need to find the probability of your ticket being selected and none of your friends' tickets being selected. Since there are 6 tickets (yours and your friends'), the probability of your ticket being chosen and none of your friends' tickets being chosen is (1/150)*(149/150)^5 = 0.00445.
The probability that none of you get a pizza lunch this month is the complement of the previous probability, which is 1 - 0.00445 = 0.99555.
The chances of you and your friends winning 3 pizza lunches in a row is the probability of winning one lunch raised to the power of 3. So, it is (1/150)^3 = 0.00000148.