Question
Download Solution PDFAn unbiased die is tossed twice then find the probability of getting a 4, 5 or 6 on the first toss and a 1, 2, 3 or 4 on the second toss ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- Probability of an event is defined as the ratio of number of cases in its favour to the total number of cases
- If A and B are two independent events then P(A ∩ B) = P(A) × P(B)
CALCULATION:
Given: An unbiased die is tossed twice.
In each case, the sample space is given by S = {1, 2, 3, 4, 5, 6}
Let E = event of getting a 4, 5 or 6 on the first toss
Let F = event of getting a 1, 2, 3 or 4 on the second toss
As we know that, probability of an event is defined as the ratio of number of cases in its favour to the total number of cases
⇒ P(E) = 3/6 = 1/2 and P(F) = 4/6 = 2/3
As we know that, if A and B are two independent events then P(A ∩ B) = P(A) × P(B)
∵ E and F are independent events
⇒ P(E ∩ F) = P(E) × P(F) = (1/2) × (2/3) = 1/3
Hence, the correct option is 4.
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