An experiment is given together with an event Find the model

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the coins (or dice) are distinguishable and fair, and that what is observed are the faces uppermost.

a) Four coins are tossed; the result is at most one tail.

b) Two dice are rolled; the numbers add to 5.

c)Two dice are rolled; the numbers add to 11.

d)Two dice are rolled; the numbers add to 13.

e) Two dice are rolled; both numbers are prime. (A positive integer is prime if it is neither 1 nor a product of smaller integers.)

Solution

1-the total no of events are 2^4=16.favourable outcomes are hhhh,hhht,thhh,hhth,hthh.so probablity=5/16.

2-the favourable outcomes are (2,3),(3,2),(4,1),(1,4).so probablity=4/36=1/9

3-the possible outcomes are (6,5),(5,6).so probablity=2/36=1/18.

4-the probablity is 0 as there are no possible outcomes.the maximum value can be12 (6,6)

5-the probablity is=(3/6)*(3/6)=1/4.the primes are 2,3,5.so in each throw we have 3 possible outcomes.

note=the total outcomes in case of dies is 6*6=36