Solution:
Total marbles = 5. Blue = 2.
P(Blue) = $\frac{2}{5}$.
2. A die is thrown. Find the probability of getting...
Solution:
Total outcomes = {1, 2, 3, 4, 5, 6}.
(i) Prime numbers: {2, 3, 5}. 3 outcomes. P(Prime) = $\frac{3}{6} = \frac{1}{2}$.
(ii) Number > 4: {5, 6}. 2 outcomes. P(>4) = $\frac{2}{6} = \frac{1}{3}$.
3. What is the probability of choosing a vowel from the alphabets?
Solution:
Total alphabets = 26. Vowels = {A, E, I, O, U} = 5.
P(Vowel) = $\frac{5}{26}$.
4. A coin is tossed...
Solution:
P(Head) = $\frac{1}{2}$.
5. The mean of 5 observations is 15... 10, 20, 15, x, 12...
Solution:
Mean = $\frac{10 + 20 + 15 + x + 12}{5} = 15$.
$57 + x = 75 \Rightarrow x = 75 - 57 = 18$.
SECTION B: LONG ANSWER (5 Marks Each)
6. Two coins are tossed simultaneously...
Solution:
Outcomes: {HH, HT, TH, TT}. Total = 4.
(i) Two Heads: {HH}. P = $\frac{1}{4}$.
(ii) At least one head: {HH, HT, TH}. P = $\frac{3}{4}$.
7. From a well-shuffled deck of 52 cards...
Solution:
(i) King of Red: {K-Heart, K-Diamond}. 2 outcomes. P = $\frac{2}{52} = \frac{1}{26}$.
(ii) Face Card: 12 cards. P = $\frac{12}{52} = \frac{3}{13}$.
(iii) Red Face Card: 6 cards. P = $\frac{6}{52} = \frac{3}{26}$.
8. In a box, there are slips numbered 1 to 10...
Solution:
(i) Multiple of 3: {3, 6, 9}. 3 outcomes. P = $\frac{3}{10}$.
(ii) Even Number: {2, 4, 6, 8, 10}. 5 outcomes. P = $\frac{5}{10} = \frac{1}{2}$.
9. The marks obtained by 10 students...
Solution:
Data: 4, 5, 6, 7, 8, 8, 8, 9, 9, 10.
Sum = 74. Mean = $7.4$.
Mode = Most Frequent = 8 (Appears 3 times).
10. A bag contains 5 green, 6 red, and 4 yellow balls...
Solution:
Total = 15.
(i) P(Red) = $\frac{6}{15} = \frac{2}{5}$.
(ii) Not Green = Red + Yellow = $6 + 4 = 10$. P = $\frac{10}{15} = \frac{2}{3}$.
SECTION C: CHALLENGERS (5 Marks Each)
11. A letter is chosen from 'MATHEMATICS'...
Solution:
Total letters = 11.
Vowels: {A, E, A, I}. (4 vowels).
P(Vowel) = $\frac{4}{11}$.
12. Two dice are thrown simultaneously. Sum of 8...
Solution:
Pairs summing to 8: (2,6), (3,5), (4,4), (5,3), (6,2).
Total pairs = 36.
P(Sum 8) = $\frac{5}{36}$.
13. There are 6 marbles 1 to 6...
Solution:
(i) P(2) = $\frac{1}{6}$.
(ii) P(5) = $\frac{1}{6}$.
14. When a spinner with three colours...
Solution:
Total sectors = 3.
P(Blue) = $\frac{1}{3}$.
15. Find the probability of getting 53 Fridays in a leap year.
Solution:
Leap year = 366 days = 52 weeks + 2 days.
The 2 remaining days can be (Mon,Tue), (Tue,Wed), ..., (Fri,Sat), (Sat,Sun), (Sun,Mon).
Total outcomes = 7.
Favorable for Friday: (Thu,Fri), (Fri,Sat). (2 outcomes).
P = $\frac{2}{7}$.