Probability Test - 5

Case (1): Event A: First is apple; second is orange. Then, P (A) = (7/21)  (14/20) = 7/30.
Case (2): Event B: First is orange; second is apple. Then, P (B) = (14/21)  (7/20) = 7/30.

So, the required probability is P (A) + P (B) = 7/15.

Since A, B or C could perform the operation independently, these are mutually exclusive events.

Therefore, the required probability is (1 - 0.5) × (1 - 0.2) × (1 - 0.3) = 0.28.

(i) The probability of an event can never be greater than 1. This statement is true as the probability of an event lies between 0 and 1 (both inclusive).

(ii) When two dice are rolled, the probability of getting the sum of 13 of two numbers appeared is 1/36. This statement is false because when two dice are rolled, the maximum number as the sum of both the numbers on the dice is 12, i.e. 6 + 6. Therefore, this is an impossible event.

(iii) In a 12-month period, the probability of a month having 31 days is 1/2. This statement is also false as there are seven months having 31 days in a year.
So, probability of a month having 31 days = 7/12

(iv) In the English alphabet, if a letter is randomly chosen, the probability that the letter is a consonant is 21/26. This statement is true as there are 21 consonants and 5 vowels in the English alphabet.

Let hills up be denoted by H and flats up be denoted by F.
Total number of outcomes = {HH, HF, FH, FF} (4 outcomes)

From the given information,
(i) Probability of no hills up = 1/4 (only one possibility out of 4)
(ii) Probability of two hills up = 1/4 (only one possibility out of 4)

Number of persons having height less than 60 inches = Number of persons having height between 48 inches and 60 inches = 13 + 9 + 23 + 10 = 55

Probability of the persons having height less than 60 inches = 55/60 = 11/12

Total number of students = 500

(a) From the table,
Number of students choosing the Business sector having Science or Arts as their stream of education = 20 + 2 = 22

Total number of students having Science or Arts as their stream = 50 + 2 + 4 + 16 + 28 + 210 + 20 + 3 + 1 + 16 = 350

So, the probability of students having Science or Arts as their stream choosing the Business sector = 22/350 = 11/175

(b) From the table,
Number of students choosing Photography as their sector = 16 + 4 + 1 = 21

So, the probability of students having Photography as their sector = 21/500

(c) From the table,
Number of Commerce students = 100 + 30 + 6 + 4 + 10 = 150

Number of students having Commerce as their stream choosing the Sports or 'Others' sector = 16

So, the probability of students having Commerce as their stream choosing the Sports or 'Others' sector with respect to all the Commerce students = 16/150 = 8/75