A die is thrown . What is the probability of getting i) a prime number? ii) a number greater than 4?
Answers
Answer:
1/2 1/3
Step-by-step explanation:
Given : A dice is thrown once.
A die has 6 faces marked as 1, 2, 3, 4, 5 and 6.
Possible outcomes are 1, 2, 3, 4, 5 and 6 = (6).
Total number Possible outcomes 6.
(i) Let E1 = Event of getting a prime number
Prime number on a dice are 2,3,5
Number of outcomes favourable to E1 = 3
Probability (E1) = Number of favourable outcomes / Total number of outcomes
P(E1) = 3/6 = ½
P(E1) = 1/2
Hence, probability of getting a prime number ,P(E1) = ½.
(ii) Let E2 = Event of getting 2 & 4
Number of outcomes favourable to E2 = 2
Probability (E2) = Number of favourable outcomes / Total number of outcomes
P(E2) = 2/6 = 1/3
P(E2) = 1/3
Hence, probability of getting 2 & 4, P(E2) = ⅓..
(iii) Let E3 = Event of getting a multiple of 2 or 3
Multiple of 2 or 3 on a dice are 2,3,4,6
Number of outcomes favourable to E3 = 4
Probability (E3) = Number of favourable outcomes / Total number of outcomes
P(E3) = 4/6 = 2/3
P(E3) = 2/3
Hence, probability of getting a multiple of 2 or 3 , P(E3) = ⅔ .
(iv) Let E4 = Event of getting an even prime number
Even Prime number on a dice are 2
Number of outcomes favourable to E4 = 1
Probability (E4) = Number of favourable outcomes / Total number of outcomes
P(E4) = 1/6
Hence, probability of getting an even prime number, P(E4) = ⅙ .
(v) Let E5 = Event of getting a number greater than 5
A number greater than 5 on a dice is 6
Number of outcomes favourable to E5 = 1
Probability (E5) = Number of favourable outcomes / Total number of outcomes
P(E5) = 1/6
Hence, probability of getting a number greater than 5 , P(E5) = ⅙ .
(vi) Let E6 = Event of getting a number lying between 2 and 6
Number lying between 2 and 6 on a dice are 3,4,5
Number of outcomes favourable to E6 = 3
Probability (E6) = Number of favourable outcomes / Total number of outcomes
P(E6) = 3/6 = ½
P(E6) = 1/2
Hence, probability of getting a number lying between 2 and 6, P(E6) = ½.
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Answer:
I){1,2,3,5}=4/6=2/3
ii){5,6}=2/6=1/3