 education

# Problems on propability

(1) A bag contains 2 red and 3 identical balls, what is the probability that in the first draw a green was picked?](2) A regular tetrahedron (4 faces) is tossed. if the four faces are labeled 1, 2, 3 and 4. find the probability that the face labeled 2 shows after one toss.
(3) in question 2 above, if we substitute the octahedron, (8 faces ) in place of tetrahedron, what is the probability that the face labeled 6 shows up after one toss?
(4) if a coin is tossed twice, what is the probability that a tail and a head show up?
(5) if the probability of living up to 60 years is 7/10, we say the odds in favour of living up to 60 years 7:3. what is the odds against living up to 60 years?
(6) What is the probability that an icosahedron (20 faces) labeled 1, 2, 3, …….20 will show the face labeled 14 if tossed only once?
(7) in a class of 40, 30 are boys. What is the probability that a girl is picked randomly to represent the girls in a debate?
(8) in a properly shuffled deck of 50 cards, what is the probability that: (a) a jack is drawn (b) an ace of Clubs is drawn?
(9) x grey balls and y blue balls are in a bag. if one is drawn at random, what is the probability that it is grey?
(10) a fair die has its faces marked 1, 1, 1, 2, 2 and 3. what is the probability that when thrown it shows a 1?
(11) A letter is chosen at random from the letters NIGERIA. what is the probability that it is (a) N (b) I
(12) a number is selected at random from the numbers 2 to 10 inclusive. find the probability that the number chosen is (a) odd (b) a multiple of 3 (c) prime (d) not a prime
(13) if a die is thrown along with a coin, what are the possible outcomes of this experiment? Perform this experiment 120 times and find the probability of obtaining a six and a tail?

6) Icosahedra (20 faces) labeled 1 to 20 if tossed once, probability of 14 appearing is = 1/20 = 1/20
7) in a class of 40,
30 = boys
Probability that a girl will be picked randomly = 40 – 30/40 = 10/40 = 1/4
8) (a) a jack is drawn, i.e only one card
Number of favourable outcomes, i.e a jack is 4 out of 52 cards.
Therefore, probability of getting ‘a jack’
P[B] = number of favorable outcomes/ total number of possible outcome = 4/52 = 1/13
(b) An ace of Club is drawn.
Ace of club = i.e one
= One out of 52 = 1/52
9) Number of grey/number of possible outcome
= x/x + y
10) Face mark = 1, 1, 1, 2, 2, 3
= number of one  / total number of face
= 3/6 = 1/2
11) Probability of
(i) N = 1 [number of N repeated]/7[total number](ii) I = 2/7

12) (a) 2, 3, 4, 5, 6, 7, 8, 9 and 10
odd = [3,5,7,9] 4 = 4/9
(b) Multiple of 3 are 3, 6, 9
3 x 1 = 3
3 x 2 = 6
3 x 3 = 9 3/9 = 1/3
(c) Prime numbers are 4, 6, 8, 9, 10
= 4/9
(d) Not a prime are = 4, 6, 8, 9, 10
= 5/9
13) if a die is thrown with a coin, possible outcome = 1/62
= 1/36
Perform this experiment 120 times = T (6) x 120
14) (a) 5 + 10 + 20 + 15 + 5 = 55 students
(i) For 16years old = 10/55 = 2/11
(ii) 18 years = 15/55 = 3/11
(b) Students in the modal age = highest age/total students