A fair die is tossed twice Find the probability of getting a

A fair die is tossed twice. Find the probability of getting at most 3 on the first tom and neither 3 nor 6 on the second toss. A couple plans to haw throe children. Construct a tree diagram and list the sample space. Find the probability that the family has no girls; at least one girl; either one girl or two boys. Conditional probability (Bayes\' rule). In a certain college town, 50% of the boys and 80% of the girls are studying mathematics. The girls constitute 60% of the student body. If a student is chosen at random and a studying mathematics, determine the probability that the student is a girl.

Solution

Answer-1)

Number of favorable outcomes
P(E1) =   Total number of possible outcome

Number of Possible Outcomes = Two different dice are thrown simultaneously being number 1, 2, 3, 4, 5 and 6 on their faces. We know that in a single thrown of two different dice, the total number of possible outcomes is (6 × 6) = 36.

Number of Favourable outcomes:

(1,1),(2,1),(3,1),(1,2),(2,2),(3,2),(1,4),(2,4),(3,4),(1,5),(2,5),(3,5) = 12

p(E₁)= 12/36

= 1/3 (Answer)

Answer-2)

There are in fact eight possible outcomes:

GGG,GGB,GBG,BGG,BBB,BBG,BGB,GBB

G stands For Girl And B stands for Boy

Probability for No Girls:     Number of favorable outcomes
Total number of possible outcome

P(E_{no girls})= 1/8

P(E_{at least one girl})= 7/8

P(E_{either One Girl or Two Boys})= 3/8