A six-sided cube is rolled. What is the probability that the number is odd or less than 4?Event A: Numbers on a six-sided cube are odd: 1, 3, 5Event B: Numbers on a six sided cube are less than 4: 1, 2, 3 1/2 2/3 5/6 1
Question
A six-sided cube is rolled. What is the probability that the number is odd or less than 4?Event A: Numbers on a six-sided cube are odd: 1, 3, 5Event B: Numbers on a six sided cube are less than 4: 1, 2, 3 1/2 2/3 5/6 1
Solution
The question is asking for the probability of two events: the number being odd (Event A) and the number being less than 4 (Event B).
Event A: The numbers on a six-sided cube that are odd are 1, 3, and 5. That's 3 out of 6 possibilities, so the probability of this event is 3/6 or 1/2.
Event B: The numbers on a six-sided cube that are less than 4 are 1, 2, and 3. That's also 3 out of 6 possibilities, so the probability of this event is also 3/6 or 1/2.
However, we can't just add these probabilities together, because there is overlap between the two events (the numbers 1 and 3 are both odd and less than 4).
So, we need to use the formula for the probability of either of two events occurring: P(A or B) = P(A) + P(B) - P(A and B).
The probability of both events occurring (Event A and Event B) is the probability of rolling a 1 or a 3, which is 2 out of 6, or 1/3.
So, the probability of rolling an odd number or a number less than 4 is (1/2) + (1/2) - (1/3) = 2/3.
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