7 It is known that, on average, one match box in 10 contains fewer than 42 matches. Eight boxes are selected, and the number of boxes that contain fewer than 42 matches is denoted by \(Y\).
- State two conditions needed to model \(Y\) by a binomial distribution.
Assume now that a binomial model is valid.
- Find
(a) \(\mathrm { P } ( Y = 0 )\),
(b) \(\mathrm { P } ( Y \geqslant 2 )\). - On Wednesday 8 boxes are selected, and on Thursday another 8 boxes are selected. Find the probability that on one of these days the number of boxes containing fewer than 42 matches is 0 , and that on the other day the number is 2 or more.